A survey taken by 150 people revealed that 65 like apple juice while 85 dislike it. One person is randomly chosen from this group. What is the chance that the chosen person dislikes apple juice? Write your answer as a ratio in simplest form.(1 point)
The probability of choosing a person who dislikes apple juice can be found by dividing the number of people who dislike apple juice (85) by the total number of people (150).
Probability of disliking apple juice = 85/150
This can be simplified by dividing both the numerator and denominator by 5:
Probability of disliking apple juice = 17/30
Therefore, the chance of choosing a person who dislikes apple juice is 17/30.
A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in the simplest form of fraction.(1 point)
A letter is to be randomly picked from the word MISSISSIPPI. Which set of letters have equal chances to be selected?(1 point)
Each individual letter in the word MISSISSIPPI is not equally likely to be selected, as some letters appear more than once. However, if we consider the distinct letters in the word (i.e. each letter only once), then the set of letters {M, I, S, P} all have an equal chance of being selected.
There are 4 distinct letters in the word MISSISSIPPI, and each distinct letter appears only once in the set {M, I, S, P}. Therefore, the probability of selecting any one of these letters is 1/4, and they all have equal chances of being selected.
A six-sided number cube is rolled 30 times and lands on 3 ten times and on 5 eight times. Calculate the experimental probability of landing on a 3. Write your answer in the simplest form of a fraction.(1 point)
The experimental probability of landing on a 3 can be calculated by dividing the number of times the cube lands on 3 (10) by the total number of rolls (30):
Experimental probability of landing on a 3 = number of times cube lands on 3 / total number of rolls
= 10/30
This fraction can be simplified by dividing both the numerator and denominator by 10:
Experimental probability of landing on a 3 = 1/3
Therefore, the experimental probability of landing on a 3 is 1/3.
The experiment involved tossing three coins simultaneously. The experiment was carried out 100 times, and it was noted that three heads occurred 40 times. What is the difference between the experimental probability of getting three heads and its theoretical probability? Write the answer in the simplest form of fraction.(1 point)
The theoretical probability of getting three heads when tossing three coins simultaneously can be found by multiplying the probability of getting a head on each individual coin:
Theoretical probability of getting three heads = (1/2) x (1/2) x (1/2) = 1/8
The experimental probability of getting three heads can be found by dividing the number of times three heads occurred by the total number of experiments:
Experimental probability of getting three heads = 40/100 = 2/5
The difference between the experimental and theoretical probabilities can be calculated by subtracting the theoretical probability from the experimental probability:
2/5 - 1/8
We can find a common denominator of 40:
(16/40) - (5/40) = 11/40
Therefore, the difference between the experimental and theoretical probabilities of getting three heads is 11/40.
An experiment involves picking a card from the number cards 2, 4, 6, 10. In equation form. What is the probability model for this experiment?(1 point)
f(x)= , where x=2, 4, 6, 10
The probability model for this experiment can be expressed as:
f(x) = P(picking card x)
where x represents the possible outcomes of the experiment (i.e. the number cards 2, 4, 6, 10).
Since each card has an equal chance of being selected, the probability of picking each of the four cards is 1/4. Therefore, the probability model can be expressed as:
f(x) = 1/4, where x = 2, 4, 6, 10
Suppose the probability of selecting a supermarket shopper who prefers plastic bags instead of paper bags is 50%. Out of 150 shoppers, how many can you expect will prefer plastic bags?(1 point)
If the probability of selecting a supermarket shopper who prefers plastic bags instead of paper bags is 50%, we can expect that 50% of the shoppers will prefer plastic bags.
To find how many out of 150 shoppers we can expect to prefer plastic bags, we can multiply the total number of shoppers by the probability of preferring plastic bags:
Expected number of shoppers who prefer plastic bags = 150 x 0.5
Expected number of shoppers who prefer plastic bags = 75
Therefore, we can expect that 75 shoppers out of 150 will prefer plastic bags.
A spinner has 8 equally sized sections labelled as A, B, C, D, E, F, G, H. In 160 spins, how many times can you expect to spin on a consonant?(1 point)
Of the 8 sections on the spinner, 5 are labelled with consonant letters (B, C, D, F, G) and 3 are labelled with vowel letters (A, E, H).
The probability of spinning on a consonant can be found by dividing the number of consonant sections by the total number of sections:
Probability of spinning on a consonant = 5/8
To find how many times we can expect to spin on a consonant in 160 spins, we can multiply the total number of spins by the probability of spinning on a consonant:
Expected number of spins on a consonant = 160 x 5/8
Expected number of spins on a consonant = 100
Therefore, we can expect to spin on a consonant 100 times out of 160 spins.
A single coin is tossed 300 times. Heads were observed 180 times. What is the long-run relative frequency of tails? Express the answer in decimal form.(1 point)
The long-run relative frequency of tails can be found by subtracting the relative frequency of heads from 1, since there are only two possible outcomes (heads or tails) and their sum must be 1.
The relative frequency of heads in this experiment is 180/300 = 0.6.
Therefore, the long-run relative frequency of tails is:
1 - 0.6 = 0.4
So the long-run relative frequency of tails is 0.4 (or 40%).
An experiment involves picking a card from a selection of cards numbered 5, 10, and 15. In equation form, what is the probability model for this experiment? List the values of x in ascending order.(2 points)
f(x)= , where x = , ,
The probability model for this experiment can be expressed as:
f(x) = P(picking card x)
where x represents the possible outcomes of the experiment (i.e. the number cards 5, 10, and 15).
Since each card has an equal chance of being selected, the probability of picking each of the three cards is 1/3. Therefore, the probability model can be expressed as:
f(x) = 1/3, where x = 5, 10, 15
So the probability model in equation form is:
f(x) = 1/3, where x = 5, 10, 15
Note that the values of x are listed in ascending order.
If the table below represents a probability model based on observed frequencies, what is the value of x?
Y C A R E S
P(Y) 0.25 0.18 0.30 0.17 x(1 point)
The sum of all the probabilities in a probability model must be equal to 1. Therefore, if we add the probabilities given in the table, we get:
0.25 + 0.18 + 0.3 + 0.17 + x = 1
Simplifying, we get:
0.9 + x = 1
Subtracting 0.9 from both sides, we get:
x = 0.1
Therefore, the value of x is 0.1.
Use the table to answer the question.
Number of White Balls Selected Number of Red Balls Selected
Bowl A 45 55
Bowl B 60 40
Bowls A and B contain a number of white and red balls. Clark repeatedly selected a ball from both bowls and recorded the results in a table. If there are 500 balls in Bowl B, what is the estimated difference in the expected number of white and red balls in Bowl B?
(1 point)
The proportion of white balls in Bowl A can be found by dividing the number of white balls by the total number of balls in the bowl:
Proportion of white balls in Bowl A = 45 / (45 + 55) = 0.45
Similarly, the proportion of white balls in Bowl B can be found by dividing the number of white balls by the total number of balls in the bowl:
Proportion of white balls in Bowl B = 60 / (60 + 40) = 0.6
The expected number of white balls in Bowl B can be estimated by multiplying the proportion of white balls in Bowl B by the total number of balls in Bowl B:
Expected number of white balls in Bowl B = 0.6 * 500 = 300
Similarly, the expected number of red balls in Bowl B can be estimated by multiplying the proportion of red balls in Bowl B by the total number of balls in Bowl B:
Expected number of red balls in Bowl B = 0.4 * 500 = 200
The estimated difference in the expected number of white and red balls in Bowl B is:
Expected number of white balls - Expected number of red balls = 300 - 200 = 100
Therefore, the estimated difference is 100.
There are a total of 5 + 6 + 7 = 18 flowers in the vase.
To find the probability of selecting two carnations, we need to find the number of ways to choose 2 carnations out of the 6 carnations, out of the total possible ways of choosing any 2 flowers out of the 18 flowers. We don't replace the flowers after selecting them, so the number of ways to choose the two carnations will depend on the previous selection.
The number of ways to choose any 2 flowers out of the 18 flowers can be found using combinations:
Number of ways to choose 2 flowers out of 18 = (18 choose 2) = 153
The number of ways to choose 2 carnations out of 6 carnations can be found using combinations:
Number of ways to choose 2 carnations out of 6 = (6 choose 2) = 15
Therefore, the probability of selecting two carnations is:
P(selecting 2 carnations) = number of ways to choose 2 carnations out of 6 / number of ways to choose 2 flowers out of 18
P(selecting 2 carnations) = 15/153
This fraction can be simplified by dividing both the numerator and denominator by 3:
P(selecting 2 carnations) = 5/51
Therefore, the probability of selecting two carnations is 5/51.
A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.(1 point)
The probability of drawing a diamond card on the first draw is 13/52, since there are 13 diamond cards in the deck out of 52 total cards.
After the first draw, there are 51 cards left, of which 12 are diamond cards (since one was already drawn). So the probability of drawing a second diamond card, given that the first card was a diamond, is 12/51.
To find the probability of drawing two diamond cards, we need to multiply these probabilities:
P(drawing two diamond cards) = (13/52) * (12/51)
P(drawing two diamond cards) = 0.0588...
Converting this decimal to a percent and rounding to the nearest hundredth, we get:
P(drawing two diamond cards) ≈ 5.88%
Therefore, the probability of drawing two diamond cards is approximately 5.88%.
Nicole pulls a colored marble out of a bowl, choosing the marble at random. There are 120 marbles in the bowl, of which 80 are black, 28 are white, and the rest are red. Use words and numbers to describe the probability that she will pull a red marble out of the bowl. Show your work.(4 points)
The probability of pulling a red marble out of the bowl can be calculated as follows:
Number of red marbles = Total number of marbles – Number of black marbles – Number of white marbles
Number of red marbles = 120 – 80 – 28
Number of red marbles = 12
Therefore, there are 12 red marbles in the bowl.
The probability of pulling a red marble can be found by dividing the number of red marbles by the total number of marbles:
Probability of pulling a red marble = Number of red marbles / Total number of marbles
Probability of pulling a red marble = 12 / 120
Probability of pulling a red marble = 0.1 or 10%
Therefore, the probability that Nicole will pull a red marble out of the bowl is 0.1 (or 10%). This means that out of 10 random selections, we would expect 1 of them to be a red marble, on average.