Question

While investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time. Additionally, 65 percent of the flights are overbooked, and 72 percent are late or not overbooked.
One Sonic Air flight will be selected at random. What is the probability that the flight selected will be late and not overbooked?

a. 0.21
b. 0.23
c. 0.26
d. 0.38
e. 0.72

Answer 1

Answer:

b

Step-by-step explanation:

draw a tree diagram to help visualize this problem. all you have to do if use the classic or formula: a+b-a(b), but use .72 as the answer and solve for a(b). so, .6 (late)+.35 (not overbooked) - ?= .72. once you solve it's .95-.72, which is .23.

Answer 2

Answer:

Option B.

Step-by-step explanation:

Let A and B represent the following events.

A = Flight is late

B = Flight is not overbooked.

It is given that 15% of the flights arrive early and 25% arrive on time. It means remaining 60% of the flights arrive late.

$P(A)=\dfrac{60}{100}=0.60$

65% of the flights are overbooked. It means reining 35% are not overbooked.

$P(B)=\dfrac{35}{100}=0.35$

72% are late or not overbooked.

$P(A\cup B)=\dfrac{72}{100}=0.72$

Using the formula of union.

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

$0.72=0.60+0.35-P(A\cap B)$

$0.72=0.95-P(A\cap B)$

$P(A\cap B)=0.95-0.72$

$P(A\cap B)=0.23$

The probability that the flight selected will be late and not overbooked is 0.23.

Therefore, the correct option is B.