A survey was conducted to determine students’ preferred learning style. The distribution of responses from the sample participants are summarized as follows:
Learning Styles Number of Students Who Prefer Each Style
auditory learning style 17
visual learning style 20
kinesthetic learning style 13
Write a ratio that compares the number of students who preferred a visual learning style to the number of student-participants of the survey. Write your answer in the simplest fraction form.(1 point)
The ratio of students who preferred a visual learning style to the total number of student-participants in the survey is:
20 : (17+20+13)
Simplifying the ratio by finding the greatest common factor of 17, 20, and 13, we get:
20 : 50
Dividing both terms by 10, we get:
2 : 5
Therefore, the ratio of students who preferred a visual learning style to the total number of student-participants is 2/5.
Each letter of the word movers is written on an individual paper strip and placed in a box. Which set represents the favorable outcomes of the event of randomly choosing a consonant letter?(1 point)
The consonant letters in the word "movers" are M, V, R, and S. Therefore, the set representing the favorable outcomes of the event of randomly choosing a consonant letter is:
{M, V, R, S}
There are 25 balls in a jar. Twelve (12) balls are red, 10 balls are blue, and 3 balls are white. Which of the following describes the likelihood of randomly picking a white ball?(1 point)
Responses
Which event is most likely to happen?(1 point)
Responses
getting a 6 when rolling a single dice once
randomly picking a vowel letter from the English alphabet
randomly picking a consonant from the English alphabet
getting a head from a single toss of a fair coin
Randomly picking a consonant from the English alphabet is the most likely event to happen as there are 21 consonants in the English alphabet compared to only 5 vowels.
On a science quiz, David got 45 out of 70 items correct. What is the empirical probability of his incorrect responses? Write your answer in the simplest form of a fraction.(1 point)
The empirical probability of David's incorrect responses is the ratio of the number of incorrect responses to the total number of responses:
Total number of responses = 70
Number of correct responses = 45
Therefore, the number of incorrect responses is:
Number of incorrect responses = Total number of responses - Number of correct responses
Number of incorrect responses = 70 - 45
Number of incorrect responses = 25
So the empirical probability of his incorrect responses is:
Empirical probability of incorrect responses = Number of incorrect responses / Total number of responses
Empirical probability of incorrect responses = 25 / 70
Simplifying the fraction by finding the greatest common factor of 25 and 70, we get:
Empirical probability of incorrect responses = 5 / 14
Therefore, the empirical probability of David's incorrect responses is 5/14 in simplest form.
Hazel has 15 T-shirts and 10 short-sleeve blouses in her wardrobe. What is the relative frequency of her T-shirts? Write your answer in decimal form.(1 point)
The relative frequency of Hazel's T-shirts is the proportion of T-shirts in her entire wardrobe:
Total number of clothing items in wardrobe = 15 + 10 = 25
Number of T-shirts in wardrobe = 15
Relative frequency of T-shirts = Number of T-shirts / Total number of clothing items
Relative frequency of T-shirts = 15 / 25
Dividing both the numerator and the denominator by the greatest common factor of 15 and 25, we get:
Relative frequency of T-shirts = 3 / 5
Expressing this fraction as a decimal, we get:
Relative frequency of T-shirts = 0.6
Therefore, the relative frequency of Hazel's T-shirts is 0.6.
A six-sided number cube is to be rolled 30 times. How many times do you expect to roll on an even number?(1 point)
Since a six-sided number cube has six possible outcomes and we are rolling the cube 30 times, we can expect to land on an even number half of the time.
Half of 30 is 15, so we can expect to roll an even number 15 times.
Therefore, we expect to roll on an even number 15 times.
A survey was conducted with 150 respondents that asked about their favorite activities during winter. There were 30 people who favored building a snowman, 80 people who liked skiing, and 40 who preferred sledding. What is the experimental probability that someone’s favorite activity is sledding? Write your answer in the simplest form of fraction.(1 point)
The experimental probability of someone's favorite activity being sledding is the ratio of the number of people who preferred sledding to the total number of respondents:
Number of people who preferred sledding = 40
Total number of respondents = 150
Experimental probability of favorite activity being sledding = Number of people who preferred sledding / Total number of respondents
Experimental probability of favorite activity being sledding = 40 / 150
Simplifying the fraction by finding the greatest common factor of 40 and 150, we get:
Experimental probability of favorite activity being sledding = 4 / 15
Therefore, the experimental probability of someone's favorite activity being sledding is 4/15 in simplest form.
Colors Where the Spinner Stopped Frequency
blue 20
red 15
green 45
yellow 10
black 15
white 45
Total 150A color wheel with six equal sections, blue, red, green, yellow, black, and white, was spun 150 times. The results are summarized in the table.
What is the experimental probability of landing on white? Express your answer in percent form.(1 point)
The experimental probability of landing on white is the ratio of the number of times white was landed on to the total number of spins:
Number of times white was landed on = 45
Total number of spins = 150
Experimental probability of landing on white = Number of times white was landed on / Total number of spins
Experimental probability of landing on white = 45 / 150
Simplifying the fraction by dividing both the numerator and the denominator by 15, we get:
Experimental probability of landing on white = 3 / 10
To express this probability as a percentage, we multiply by 100:
Experimental probability of landing on white = 3 / 10 × 100%
Experimental probability of landing on white = 30%
Therefore, the experimental probability of landing on white is 30% in percent form.
A calculator manufacturing company checks 500 calculator units, and 25 of them have non-functioning keys. Approximate the relative frequency of a non-defective unit from this batch of items. Express your answer in the simplest form of a fraction.(1 point)
The relative frequency of a non-defective unit is the proportion of units that are not defective in the entire batch:
Total number of units = 500
Number of defective units = 25
Number of non-defective units = Total number of units - Number of defective units
Number of non-defective units = 500 - 25
Number of non-defective units = 475
Therefore, the relative frequency of a non-defective unit is:
Relative frequency of non-defective unit = Number of non-defective units / Total number of units
Relative frequency of non-defective unit = 475 / 500
Simplifying the fraction by finding the greatest common factor of 475 and 500, we get:
Relative frequency of non-defective unit = 19 / 20
Therefore, the relative frequency of a non-defective unit is 19/20 in simplest form.
You toss a coin 50 times and get 12 tails. What is the empirical probability of getting heads? Write your answer in percent form.(1 point)
Responses
The empirical probability of getting heads is the ratio of the number of times we got heads to the total number of coin tosses:
Total number of coin tosses = 50
Number of times we got tails = 12
Number of times we got heads = Total number of coin tosses - Number of times we got tails
Number of times we got heads = 50 - 12
Number of times we got heads = 38
Therefore, the empirical probability of getting heads is:
Empirical probability of getting heads = Number of times we got heads / Total number of coin tosses
Empirical probability of getting heads = 38 / 50
To express this probability as a percentage, we multiply by 100:
Empirical probability of getting heads = 38 / 50 × 100%
Empirical probability of getting heads = 76%
Therefore, the empirical probability of getting heads is 76% in percent form.
A quality controller inspected 1,000 units of a product and rejected 150 units due to defects. Approximate the empirical probability that a unit will pass the inspection.(1 point)
Responses
The empirical probability that a unit will pass the inspection is the proportion of units that are accepted in the entire batch:
Total number of units = 1000
Number of defective units = 150
Number of accepted units = Total number of units - Number of defective units
Number of accepted units = 1000 - 150
Number of accepted units = 850
Therefore, the empirical probability that a unit will pass the inspection is:
Empirical probability of unit passing inspection = Number of accepted units / Total number of units
Empirical probability of unit passing inspection = 850 / 1000
Simplifying the fraction by dividing both the numerator and the denominator by 50, we get:
Empirical probability of unit passing inspection = 17 / 20
Therefore, the empirical probability that a unit will pass the inspection is 17/20.
In which scenario is the experimental probability equal to the theoretical probability?(1 point)
The experimental probability will be equal to the theoretical probability in situations when the actual outcomes of an experiment are in line with the expected outcome based on theoretical probability. An example of such a scenario is when rolling a fair six-sided die where each face has an equal chance of landing face-up. In this situation, the theoretical probability of rolling any one number is 1/6, and if the die is rolled a large number of times, the experimental probability of rolling each number is likely to be very close to 1/6. Therefore, the experimental probability will be equal to the theoretical probability in situations where the random events are determined by a known probability distribution, and the sample size is large enough to smooth out any variations or randomness in the data.
As part of a promotion, people who participate in a survey are sent a free coupon for one of three winter activities: skiing, snow tubing, or sleigh rides. Participants have an equal chance of receiving each type of coupon. If 900 people participate, how many would be expected to receive a coupon for sleigh rides?(1 point)
Since participants have an equal chance of receiving each type of coupon, and there are three types of coupons, each coupon has a probability of 1/3 of being given out.
If 900 people participate, then we can expect that 1/3 of them will receive a coupon for sleigh rides:
Expected number of people receiving a coupon for sleigh rides = (1/3) × 900
Simplifying the expression on the right, we get:
Expected number of people receiving a coupon for sleigh rides = 300
Therefore, we can expect 300 people to receive a coupon for sleigh rides.
The letter tiles C, A, R, E, S are placed in a box. Without looking, Jorelle picks a letter tile from the box and records the result before placing it back. If he repeats the procedure 100 times, how many times will the letter A tile be picked?(1 point)
Since Jorelle picks a letter tile and records the result before placing it back, it means that each pick is an independent event with a probability of 1/5 of picking the letter A tile.
If Jorelle repeats the procedure 100 times, we can expect the number of times the letter A tile is picked to be:
Expected number of times A tile is picked = Probability of picking A tile × Total number of picks
Expected number of times A tile is picked = (1/5) × 100
Simplifying the expression on the right, we get:
Expected number of times A tile is picked = 20
Therefore, we can expect the letter A tile to be picked 20 times.
The letter tiles W, I, S, D, O, M are placed on a box. Without looking, Abby picks a letter tile from the box. What is the probability that the letter she picks is a vowel? Write your answer in the simplest form of a fraction.(1 point)
The letter tiles in the box are W, I, S, D, O, and M.
Out of these six letters, I and O are vowels (letters that represent speech sounds produced by an open configuration of the vocal tract), so the probability of picking a vowel is:
Probability of picking a vowel = Number of vowels / Total number of letters
Number of vowels = 2 (I and O)
Total number of letters = 6
Substituting these values, we get:
Probability of picking a vowel = 2 / 6
Simplifying the fraction by finding the greatest common factor of 2 and 6, we get:
Probability of picking a vowel = 1 / 3
Therefore, the probability of Abby picking a vowel is 1/3 in simplest form.
The sample space of an experiment is S={1,2,3}. Each outcome is equally likely to occur with a probability of 13. What is the probability of picking number 2 or 3? Write your answer in the simplest form of a fraction.(1 point)
The probability of picking number 2 or 3 is the sum of the probabilities of picking 2 and picking 3, since these outcomes are mutually exclusive (i.e., you can't pick both at the same time).
Since each outcome is equally likely to occur, and there are three outcomes in the sample space, the probability of each outcome is 1/3.
Therefore, the probability of picking number 2 or 3 is:
Probability of picking 2 or 3 = Probability of picking 2 + Probability of picking 3
Probability of picking 2 or 3 = (1/3) + (1/3)
Adding the fractions, we get:
Probability of picking 2 or 3 = 2/3
Therefore, the probability of picking number 2 or 3 is 2/3.
Mr. Lim has a bag with some marbles colored red, yellow, green, blue, and white. The marbles are identical in number. If there are 40 marbles in the bag, how many marbles of each color are in the bag?(1 point)
Since all the marbles are identical in number and there are five different colors, the number of marbles of each color is the same.
Let's call the number of marbles of each color "x". Then, we can write an equation based on the total number of marbles in the bag:
Number of red marbles + Number of yellow marbles +Number of green marbles + Number of blue marbles + Number of white marbles = Total number of marbles
x + x + x + x + x = 40
Simplifying the expression on the left side, we get:
5x = 40
Dividing both sides by 5, we get:
x = 8
Therefore, there are 8 marbles of each color in the bag.
The sample space of an experiment is S={a, b, c, d, e, f}. What is the probability of picking a consonant? Write your answer in the simplest fraction form.(1 point)
A consonant is any letter of the alphabet that is not a vowel (i.e., a, e, i, o, u).
In the sample space S={a, b, c, d, e, f}, there are four consonants: b, c, d, and f.
Since the sample space has six elements, each with the same probability, the probability of picking a consonant is:
Probability of picking a consonant = Number of consonants / Total number of elements in the sample space
Number of consonants = 4
Total number of elements in the sample space = 6
Substituting these values, we get:
Probability of picking a consonant = 4 / 6
Simplifying the fraction by finding the greatest common factor of 4 and 6, we get:
Probability of picking a consonant = 2 / 3
Therefore, the probability of picking a consonant is 2/3 in simplest fraction form.
Use the table to answer the question.
Letters M O D E L S
Probability 16 16 16 16 16 16
Use the uniform probability model to find the probability of selecting a vowel letter from the word MODELS.
(1 point)
Out of the letters in the word MODELS, the vowels are O and E.
Each of the letters has a probability of 1/6 of being selected based on the uniform probability model.
Therefore, the probability of selecting a vowel letter is the sum of the individual probabilities of selecting O and E:
Probability of selecting a vowel letter = Probability of selecting O + Probability of selecting E
Probability of selecting a vowel letter = 1/6 + 1/6
Probability of selecting a vowel letter = 2/6
Simplifying the fraction by finding the greatest common factor of 2 and 6, we get:
Probability of selecting a vowel letter = 1/3
Therefore, the probability of selecting a vowel letter from the word MODELS is 1/3.
A deck of 10 cards labeled 1–10 is shuffled. One card is selected at random. If the experiment is repeated 120 times, how many times will you expect to select number 5?(1 point)
Since there are 10 cards labeled 1-10 and each card has an equal chance of being selected, the probability of selecting any one card is 1/10.
If the experiment of selecting a card is repeated 120 times, we can expect the number of times
Letter tiles H, O, N, E, S, T are shuffled and placed in a box. A letter is selected at random. What is the probability of selecting letter A?(1 point)
Responses