Q: Given $P(A) = 0.35$, $P(B) = 0.35$, and $A$ and $B$ are independent, what is $P(A \cup B)$?

$0.35 + 0.35 - (0.35 \times 0.35)$

Question 1

A call center offers two types of credit cards: travel and cashback. The probability a caller qualifies for a travel card is 0.40, and for a cashback card is 0.35. What is the probability that a randomly selected caller qualifies for either card, assuming no one qualifies for both?

Accepted Answer

$0.75$

Question 2

Suppose you toss two fair coins. What is the probability that both coins show tails?

Accepted Answer

$0.25$

Question 3

If events $A$ and $B$ are independent, which of the following equations must be true?

Accepted Answer

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

Question 4

A company insures 5 buildings, each with a 5% chance of fire damage in a year. Assuming independence, what is the probability that at least one building has fire damage in a year?

Accepted Answer

$1 - (0.95)^5$

Question 5

Which of the following statements is TRUE about mutually exclusive (disjoint) events $A$ and $B$?

Accepted Answer

$P(A \cap B) = 0$

Question 6

A store survey shows 130 females prefer iPads, 91 females prefer cameras, 117 males prefer iPads, and 50 males prefer cameras. If a customer is selected at random, what is the probability that the customer is a female who prefers a camera?

Accepted Answer

$\frac{91}{388}$

Question 7

Given $P(A) = 0.35$, $P(B) = 0.35$, and $A$ and $B$ are independent, what is $P(A \cup B)$?

Accepted Answer

$0.35 + 0.35 - (0.35 	imes 0.35)$

Question 8

If $P(A) = 0.68$, $P(B) = 0.56$, and $P(A \cap B) = 0.49$, what is $P(A | B)$?

Accepted Answer

$\frac{0.49}{0.56}$

Question 9

A building has a 2% chance of experiencing a fire in a year, and if there is a fire, there is a 70% chance it will be destroyed. What is the probability the building will be destroyed by fire in a year?

Accepted Answer

$0.70 	imes 0.02$

Question 10

If $P(A) = 0.8$ and $P(B) = 0.2$, and $A$ and $B$ are disjoint, what is $P(A \cup B)$?

Accepted Answer

$0.8 + 0.2$

Question 11

A worker is selected at random. 68% have health insurance, 56% have a retirement plan, and 49% have both. What is the probability a worker has health insurance given they have a retirement plan?

Accepted Answer

$\frac{0.49}{0.56}$

Question 12

Which of the following is the correct formula for the probability of the complement of event $A$?

Accepted Answer

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

Question 13

If you roll two dice, what is the probability of rolling a 4 on the first die and an even number on the second die?

Accepted Answer

$\frac{1}{12}$

Question 14

Which of the following best describes the difference between independent and disjoint events?

Accepted Answer

Disjoint events cannot occur together, while independent events have no effect on each other's probability.

Question 15

If $P(A) = 0.5$ and $P(B) = 0.3$, and $A$ and $B$ are independent, what is $P(A \cap B)$?

Accepted Answer

$0.15$

Question 16

A company wants to know the probability that a client pays on time. If 80% of clients pay on time, what is the probability that out of three independent clients, all pay on time?

Accepted Answer

$0.8^3$

Question 17

Given a contingency table, the probability of selecting a female who prefers a camera is called:

Accepted Answer

Joint probability

Question 18

If $P(A \cap B) = 0.2$ and $P(B) = 0.5$, what is $P(A | B)$?

Accepted Answer

$0.4$

Question 19

Which of the following is the correct general addition rule for any two events $A$ and $B$?

Accepted Answer

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Probability Fundamentals for Business Statistics

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