Q: A bag contains 3 red balls and 2 blue balls. If you randomly select one ball, what is the probability of selecting a blue ball? Use the classical probability formula.

$$P(\text{blue}) = \frac{2}{5}$$

Q: A hospital reports that the probability a patient recovers from a certain surgery is 0.85. What is the probability that a patient does NOT recover?

$$P(\text{not recover}) = 1 - 0.85 = 0.15$$

Q: If two events A and B are independent, which of the following is true?

$$P(A \cap B) = P(A) \times P(B)$$

Q: A card is drawn from a standard deck. What is the probability that it is either a heart or a king? (Assume there are no overlaps in the events.)

$$P(\text{heart or king}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$$

Q: A die is rolled twice. What is the probability of getting a 6 on both rolls?

$$\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$$

Question 1

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

Accepted Answer

As the number of trials increases, the experimental probability approaches the theoretical probability.

Question 2

A bag contains 3 red balls and 2 blue balls. If you randomly select one ball, what is the probability of selecting a blue ball? Use the classical probability formula.

Accepted Answer

$$P(	ext{blue}) = \frac{2}{5}$$

Question 3

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$ using the addition rule?

Accepted Answer

$$P(A \cup B) = 0.7$$

Question 4

Which of the following is NOT a type of probability discussed in the study guide?

Accepted Answer

Relative probability

Question 5

A hospital reports that the probability a patient recovers from a certain surgery is 0.85. What is the probability that a patient does NOT recover?

Accepted Answer

$$P(	ext{not recover}) = 1 - 0.85 = 0.15$$

Question 6

If two events A and B are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 7

A card is drawn from a standard deck. What is the probability that it is either a heart or a king? (Assume there are no overlaps in the events.)

Accepted Answer

$$P(	ext{heart or king}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$$

Question 8

Which formula would you use to find the probability of the complement of event A?

Accepted Answer

$$P(A^c) = 1 - P(A)$$

Question 9

If $$P(A \mid B) = 0.6$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0.3$$

Question 10

A password consists of 3 letters followed by 2 digits. How many different passwords are possible if letters and digits can be repeated? (Use the Fundamental Counting Principle.)

Accepted Answer

$$26^3$$ 	imes $$10^2$$

Question 11

Which of the following best describes empirical probability?

Accepted Answer

Probability based on observed data from experiments.

Question 12

If two events are mutually exclusive, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0$$

Question 13

A medical test for a disease has a 95% chance of correctly identifying a diseased patient. If the probability that a randomly selected patient has the disease is 0.02, what is the probability that a randomly selected patient both has the disease and tests positive?

Accepted Answer

$$0.02 	imes 0.95 = 0.019$$

Question 14

Which of the following is the correct formula for conditional probability?

Accepted Answer

$$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$

Question 15

A die is rolled twice. What is the probability of getting a 6 on both rolls?

Accepted Answer

$$\frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$$

Chapter 3: Probability – Study Guide

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