Respuesta :
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.
[tex]P(A)=\dfrac{60}{100}=0.60[/tex]
65% of the flights are overbooked. It means reining 35% are not overbooked.
[tex]P(B)=\dfrac{35}{100}=0.35[/tex]
72% are late or not overbooked.
[tex]P(A\cup B)=\dfrac{72}{100}=0.72[/tex]
Using the formula of union.
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]0.72=0.60+0.35-P(A\cap B)[/tex]
[tex]0.72=0.95-P(A\cap B)[/tex]
[tex]P(A\cap B)=0.95-0.72[/tex]
[tex]P(A\cap B)=0.23[/tex]
The probability that the flight selected will be late and not overbooked is 0.23.
Therefore, the correct option is B.
Probability of fight being late or overbooked is given. The probability that the flight selected will be late and not overbooked is 0.23 or 23%.
Given information:
The customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time.
65 percent of the flights are overbooked, and 72 percent are late or not overbooked.
Let X be the event that "the flight is late". Y be the event that "the flight is not overbooked".
From the given information,
[tex]P(X)=60 \%=0.60[/tex]
65% flights are overbooked. So, 35% of the flight will not be overbooked.
[tex]P(Y)=35 \%=0.35[/tex]
72 percent are late or not overbooked. Mathematically, it can be written as,
[tex]P(X \cup Y)=72 \%=0.72[/tex]
Now, the probability that the flight selected will be late and not overbooked will be calculated as,
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\0.72=0.6+0.35-P(X\cap Y)\\P(X\cap Y)=0.95-0.72\\P(X\cap Y)=0.23[/tex]
Therefore, the probability that the flight selected will be late and not overbooked is 0.23 or 23%.
For more details, refer to the link:
https://brainly.com/question/23044118
