Respuesta :
Answer:
0.109 = 10.9% probability that it is raining if the flight leaves on time.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Conditional probability:
Event A: Leaves on time
Event B: Raining
Probability that the flight will be delayed is 0.08.
So 1 - 0.08 = 0.92 probability that it leaves on time, that is, [tex]P(A) = 0.92[/tex]
The probability that it will not rain and the flight will leave on time is 0.82.
0.92 - 0.82 = 0.1 probability it is raining and the flight leaves on time, so:
[tex]P(A \cap B) = 0.1[/tex]
What is the probability that it is raining if the flight leaves on time?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1}{0.92} = 0.109[/tex]
0.109 = 10.9% probability that it is raining if the flight leaves on time.
