Question

question 6
$p(a) = 0.60$, $p(b) = 0.30$, and $p(a \text{ and } b) = 0.10$.
what is $p(a \text{ or } b)$?
a. 0.80
b. 0.90
c. 0.70
d. 0.40

question 7
a pet store sells mice, reptiles, and birds.
let event a = a customer buys a mouse.
let event b = a customer buys a reptile.
what does $p(a \text{ or } b) = 0.20$ mean in terms of this problem?
a. the probability that a customer buys both a mouse and a reptile is 20%.
b. buying a mouse and buying a reptile are mutually exclusive events.
c. the probability that a customer buys neither a mouse nor a reptile is 20%.
d. the probability that a customer buys either a mouse or a reptile is 20%.

question 8
a marketing firm tracks data on grocery store visits. in one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.70, and the probability that a shopper buys cheese is 0.20.
event a = a shopper buys bread.
event b = a shopper buys cheese.
a and b are independent events if ______.
a. the probability of buying bread and cheese is 0.14
b. the probability of buying bread and cheese is 0
c. the probability of buying bread or cheese is 0.90
d. the probability of buying bread or cheese is 0.14

question 9
a and b are independent events. $p(a) = 0.50$ and $p(b) = 0.20$.
what is $p(a \text{ and } b)$?
a. 0.70
b. 0.01
c. 0
d. 0.10

Explanation:

Question 6

Step1: Apply addition rule

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

Step2: Substitute given values

$P(A \text{ or } B) = 0.60 + 0.30 - 0.10$

Step3: Calculate the result

$P(A \text{ or } B) = 0.80$

Question 7

Step1: Define $P(A \text{ or } B)$

$P(A \text{ or } B)$ represents the probability that at least one of events $A$ or $B$ occurs.

Step2: Match to context

In this problem, this means the probability a customer buys either a mouse or a reptile is 20%.

Question 8

Step1: Recall independent events rule

For independent events, $P(A \text{ and } B) = P(A) \times P(B)$

Step2: Substitute given values

$P(A \text{ and } B) = 0.70 \times 0.20$

Step3: Calculate the result

$P(A \text{ and } B) = 0.14$

Question 9

Step1: Apply independent events rule

$P(A \text{ and } B) = P(A) \times P(B)$

Step2: Substitute given values

$P(A \text{ and } B) = 0.50 \times 0.20$

Step3: Calculate the result

$P(A \text{ and } B) = 0.10$

Answer:

Question 6: A. 0.80
Question 7: D. The probability that a customer buys either a mouse or a reptile is 20%.
Question 8: A. the probability of buying bread and cheese is 0.14
Question 9: D. 0.10