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 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