Q: A box contains 15 chocolates, 12 nut candies, and 10 caramels. If two candies are chosen without replacement, what is the probability that both are caramels?

$$\frac{10}{37} \times \frac{9}{36} = \frac{90}{1332} = 0.068$$

Q: Given $$P(E) = 0.45$$ and $$P(F) = 0.20$$, what is $$P(E \text{ or } F) if E $$and F are independent?

$$0.45 + 0.20 - (0.45 \times 0.20) = 0.56$$

Q: Is it unusual for a respondent to be a Republican and say 'yes'? Why or why not?

No, because $$P(\text{Rep and Yes}) = 0.148 \u003e 0.05$$

Q: Is it unusual for a respondent to be an Independent and say 'not sure'? Why or why not?

Yes, because $$P(\text{Ind and Not Sure}) = \frac{5}{540} = 0.009 \u003c 0.05$$

Question 1

A box contains 15 chocolates, 12 nut candies, and 10 caramels. If two candies are chosen without replacement, what is the probability that both are caramels?

Accepted Answer

$$\frac{10}{37} 	imes \frac{9}{36} = \frac{90}{1332} = 0.068$$

Question 2

In a poll, 540 residents responded. If one person is randomly chosen, what is the probability that they said 'yes' to hiring more teachers?

Accepted Answer

$$\frac{137+80+75+15}{540} = \frac{307}{540} = 0.569$$

Question 3

Given $$P(E) = 0.45$$ and $$P(F) = 0.20$$, what is $$P(E 	ext{ and } F) if E $$and F are mutually exclusive?

Accepted Answer

$$0$$

Question 4

Given $$P(E) = 0.45$$ and $$P(F) = 0.20$$, what is $$P(E 	ext{ or } F) if E $$and F are mutually exclusive?

Accepted Answer

$$0.65$$

Question 5

Given $$P(E) = 0.45$$ and $$P(F) = 0.20$$, what is $$P(E 	ext{ and } F) if E $$and F are independent?

Accepted Answer

$$0.45 	imes 0.20 = 0.09$$

Question 6

Given $$P(E) = 0.45$$ and $$P(F) = 0.20$$, what is $$P(E 	ext{ or } F) if E $$and F are independent?

Accepted Answer

$$0.45 + 0.20 - (0.45 	imes 0.20) = 0.56$$

Question 7

A poll asked residents about hiring more teachers. If one person is randomly chosen, what is the probability that they are a Republican and said 'yes'?

Accepted Answer

$$\frac{80}{540} = 0.148$$

Question 8

Is it unusual for a respondent to be a Republican and say 'yes'? Why or why not?

Accepted Answer

No, because $$P(	ext{Rep and Yes}) = 0.148 \u003e 0.05$$

Question 9

Is it unusual for a respondent to be an Independent and say 'not sure'? Why or why not?

Accepted Answer

Yes, because $$P(	ext{Ind and Not Sure}) = \frac{5}{540} = 0.009 \u003c 0.05$$

Question 10

If one person is randomly chosen from the poll, what is the probability that they are a Democrat or said 'yes'?

Accepted Answer

Question 11

Which of the following pairs of events are mutually exclusive?

Accepted Answer

A person is driving a car and the same person is riding a horse.

Question 12

Which of the following pairs of events are independent?

Accepted Answer

A coin flip comes up heads and a roll of a die results in an even number.

Question 13

A household in Santa Monica has a probability of 0.38 of owning a dog. Which of the following best interprets this probability?

Accepted Answer

If we looked at 100 households in Santa Monica, we’d expect to find that 38 owned a dog.

Question 14

The probability that an oil well successfully produces oil is 0.034. Which of the following best interprets this probability?

Accepted Answer

If we looked at 1000 oil wells, we’d expect 34 of them to successfully produce oil.

Question 15

A die is rolled. Are the events 'getting an even number' and 'getting a number greater than 3' mutually exclusive?

Accepted Answer

No, because numbers like 4 and 6 are both even and greater than 3.

Question 16

A student takes a math class and the same student majors in physics. Are these events independent?

Accepted Answer

No, because a physics major is more likely to take math classes.

Question 17

If you roll a die, are the events 'getting an even number' and 'getting an odd number' mutually exclusive?

Accepted Answer

Yes, because a single roll cannot result in both an even and an odd number.

Question 18

A coin is flipped and a die is rolled. Are the events 'coin comes up heads' and 'die shows an even number' independent?

Accepted Answer

Yes, because the outcome of the coin flip does not affect the die roll.

Question 19

A box contains 15 chocolates, 12 nut candies, and 10 caramels. If one candy is randomly chosen, what is the probability that it is not a nut candy?

Accepted Answer

$$\frac{15+10}{37} = \frac{25}{37} = 0.676$$

Introductory Statistics Probability and Independence Review Guidance

Study Guide - Practice Questions

Study Guide - Flashcards