Q: If events E and F are disjoint, which formula should you use to find $$P(E \text{ or } F)$$?

$$P(E \text{ or } F) = P(E) + P(F)$$

Q: If the probability that a randomly selected 60-year-old female will survive the year is 0.992, what is the probability that two randomly selected 60-year-old females will both survive the year?

$$0.992 \times 0.992 = 0.984064$$

Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.

Question 2

Suppose you roll a fair 10-sided die 40 times and observe that the proportion of rolls resulting in a '4' is 0.15. What would you expect to happen to this proportion as you increase the number of rolls to 1000?

Accepted Answer

The proportion will get closer to the theoretical probability of rolling a '4', which is $$\frac{1}{10}.$$

Question 3

A probability model must satisfy which of the following conditions?

Accepted Answer

All probabilities are between 0 and 1, and the sum of the probabilities of all outcomes equals 1.

Question 4

If the probability of an event is 0.03, how would you classify this event?

Accepted Answer

Unusual, because its probability is less than 0.05.

Question 5

A bag contains 9 brown, 6 yellow, 7 red, 4 orange, 2 blue, and 2 green candies. What is the probability of randomly selecting a yellow candy?

Accepted Answer

$$\frac{6}{30}$$

Question 6

Which of the following is an example of a subjective probability?

Accepted Answer

An economist predicts a 20% chance of recession next year based on their judgment.

Question 7

If events E and F are disjoint, which formula should you use to find $$P(E 	ext{ or } F)$$?

Accepted Answer

$$P(E 	ext{ or } F) = P(E) + P(F)$$

Question 8

Given $$P(E) = 0.32$$, $$P(F) = 0.61$$, and $$P(E 	ext{ and } F) = 0.10$$, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.32 + 0.61 - 0.10 = 0.83$$

Question 9

If the probability that a household owns a dog is 0.316, what is the probability that a household does NOT own a dog?

Accepted Answer

$$1 - 0.316 = 0.684$$

Question 10

Which of the following statements is TRUE about independent events?

Accepted Answer

The occurrence of one event does not affect the probability of the other event.

Question 11

If the probability that a randomly selected 60-year-old female will survive the year is 0.992, what is the probability that two randomly selected 60-year-old females will both survive the year?

Accepted Answer

$$0.992 	imes 0.992 = 0.984064$$

Question 12

What is the probability that at least one of 500 randomly selected 60-year-old females will die during the year, given the probability of surviving is 0.992?

Accepted Answer

$$1 - (0.992$$)^{500}$$

Question 13

Given the Venn diagram with $$E = \{1,3,5,7,9\}$$ and $$F = \{0,1,2,3,4\}$$, what is $$P(E 	ext{ or } F) if $$the sample space $$S$$ has 10 equally likely outcomes?

Accepted Answer

$$\frac{8}{10} = 0.8$$

Question 14

If $$P(E|F) = \frac{P(E 	ext{ and } F)}{P(F)}$$, what does $$P(E|F)$$ represent?

Accepted Answer

The probability of event E occurring given that event F has occurred.

Question 15

How many different ways can you arrange the letters in the word 'MISSISSIPPI'?

Accepted Answer

$$\frac{11!}{4!4!2!1!}$$

Question 16

A restaurant offers 2 appetizers, 4 entrées, and 2 desserts. How many different meals can be ordered if you choose one of each?

Accepted Answer

$$2 	imes 4 	imes 2 = 16$$

Question 17

In a group of 10 horses, how many ways can you choose 4 to receive a treat, regardless of order?

Accepted Answer

$$\frac{10!}{4!6!}$$

Question 18

Which counting technique should you use if you are making a sequence of choices and the order matters?

Accepted Answer

Permutation

Question 19

A pizza shop offers 8 toppings. What is the probability that a randomly selected pizza with 2 toppings includes pepperoni, assuming all combinations are equally likely?

Accepted Answer

$$\frac{\binom{7}{1}}{\binom{8}{2}}$$

Chapter 5: Probability – Rules, Methods, and Applications

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