Q: Which formula correctly represents the probability of an event occurring?

$$P(E) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$

Q: A deck of cards has 52 cards. What is the probability of drawing an Ace?

$$P(\text{Ace}) = \frac{4}{52}$$

Q: If two events E and F are disjoint, which formula should be used to find the probability that either E or F occurs?

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

Q: A coin is flipped 100 times and lands on heads 48 times. What is the empirical probability of getting heads?

$$P(\text{heads}) = \frac{48}{100}$$

Q: Which rule should be used to find the probability of either event E or event F occurring if E and F are not disjoint?

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

Question 1

Which formula correctly represents the probability of an event occurring?

Accepted Answer

$$P(E) = \frac{	ext{number of favorable outcomes}}{	ext{total number of outcomes}}$$

Question 2

A fair die is rolled. What is the probability of rolling a 4?

Accepted Answer

$$P(4) = \frac{1}{6}$$

Question 3

If an event has a probability of 0, what does this mean?

Accepted Answer

The event is impossible.

Question 4

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 5

A deck of cards has 52 cards. What is the probability of drawing an Ace?

Accepted Answer

$$P(	ext{Ace}) = \frac{4}{52}$$

Question 6

If two events E and F are disjoint, which formula should be used to find the probability that either E or F occurs?

Accepted Answer

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

Question 7

Which of the following is NOT a requirement for a probability model?

Accepted Answer

Probabilities can be negative.

Question 8

A coin is flipped 100 times and lands on heads 48 times. What is the empirical probability of getting heads?

Accepted Answer

$$P(	ext{heads}) = \frac{48}{100}$$

Question 9

Which method of probability calculation requires equally likely outcomes?

Accepted Answer

The classical method

Question 10

If $$P(E) = 0.03$$, how would you describe event E?

Accepted Answer

Unusual

Question 11

If $$P(E) = 0.7$$ and $$P(F) = 0.2$$ and E and F are disjoint, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.9$$

Question 12

Which of the following best describes a sample space?

Accepted Answer

The set of all possible outcomes of an experiment.

Question 13

If the probability of an event A is 0.5, what does this mean?

Accepted Answer

Event A is equally likely to occur or not occur.

Question 14

Which of the following is an example of subjective probability?

Accepted Answer

A doctor estimates a 60% chance of recovery based on experience.

Question 15

If $$P(E) = 0.4$$, what is the probability of the complement of E?

Accepted Answer

$$0.6$$

Question 16

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

$$\frac{3}{10}$$

Question 17

Which rule should be used to find the probability of either event E or event F occurring if E and F are not disjoint?

Accepted Answer

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

Question 18

A simulation is used to estimate the probability of rain tomorrow. Which method is being used?

Accepted Answer

Empirical method

Question 19

If $$P(E) = 0.8$$ and $$P(F) = 0.3$$ and $$P(E 	ext{ and } F) = 0.1$$, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$1.0$$

Question 20

Which of the following is true about the probability of an event?

Accepted Answer

It is always between 0 and 1, inclusive.

Chapter 5: Probability – Rules, Methods, and Applications

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