Question

question 13
at a car and truck dealership, the probability that a vehicle is white is 0.25. the probability that it is a pickup truck is 0.15. the probability that it is a white pickup truck is 0.06. what is the probability that a vehicle is white, given that the vehicle is a pickup truck? round your answer to two decimal places.
a. 0.19
b. 0.06
c. 0.24
d. 0.40

question 14
a and b are independent events.
$p(a) = 0.50$
$p(b) = 0.20$
what is $p(a|b)$?
a. not enough information
b. 0.20
c. 0.10
d. 0.50

question 15
in a concert band, the probability that a member is in the brass section is 0.50. the probability that a member plays trumpet, given that he or she is in the brass section, is 0.36. what is the probability that a randomly selected band member is in the brass section and plays trumpet?
a. 0.86
b. 0.72
c. 0.18
d. 0.14

question 16
this table shows how many sophomores and juniors attended two school events.
what is the probability that a randomly chosen person from this group attended the volleyball game? round your answer to two decimal places.
a. 0.48
b. 0.31
c. 0.55
d. 0.18

Explanation:

Question 13

Step1: Recall conditional probability formula

$P(\text{White}|\text{Pickup}) = \frac{P(\text{White and Pickup})}{P(\text{Pickup})}$

Step2: Substitute given values

$P(\text{White}|\text{Pickup}) = \frac{0.06}{0.15}$

Step3: Calculate and round result

$\frac{0.06}{0.15}=0.40$

Question 14

Step1: Use independent events property

For independent events, $P(A|B)=P(A)$

Step2: Substitute given value

$P(A|B)=0.50$

Question 15

Step1: Recall joint probability formula

$P(\text{Brass and Trumpet}) = P(\text{Trumpet}|\text{Brass}) \times P(\text{Brass})$

Step2: Substitute given values

$P(\text{Brass and Trumpet}) = 0.36 \times 0.50$

Step3: Calculate result

$0.36 \times 0.50=0.18$

Question 16

Step1: Define probability formula

$P(\text{Volleyball}) = \frac{\text{Total Volleyball attendees}}{\text{Total people}}$

Step2: Substitute table values

$P(\text{Volleyball}) = \frac{66}{137}$

Step3: Calculate and round result

$\frac{66}{137}\approx0.48$

Answer:

Question 13: D. 0.40
Question 14: D. 0.50
Question 15: C. 0.18
Question 16: A. 0.48