Final answer:
To calculate the conditional probability that it is not raining given the flight has been delayed, we use P(A|B) = P(A and B) / P(B). We adjust the probabilities for the fact that we are considering 'not raining,' resulting in a probability of 0.4545, or 0.455 when rounded to the nearest thousandth.
Step-by-step explanation:
The question asks about the probability of a particular event (it not raining) given that another event (flight has been delayed) has occurred. This is a classic example of conditional probability. We can use the formula P(A|B) = P(A and B) / P(B) to find this probability, where P(A|B) is the probability of A given that B has occurred, P(A and B) is the probability of both A and B occurring, and P(B) is the probability of B occurring.
In this scenario:
- P(A) is the probability that it will not rain.
- P(B) is the probability that the flight will be delayed, which is given as 0.11.
- P(A and B) is the probability that it will rain and the flight will be delayed, which is given as 0.06.
We can find P(A), the probability that it will not rain, by subtracting the probability that it will rain from 1 (since either it rains, or it does not).
This gives us P(A) = 1 - 0.19 = 0.81, the probability that it will not rain.
We can now calculate the conditional probability P(A|B) using the formula:
P(A|B) = P(A and B) / P(B).
However, we are given P(not A and B), which is the probability that it will rain and the flight will be delayed. To adjust for this, we need to find the probability that it will not rain given that the flight is delayed. We calculate this by subtracting P(A and B) from P(B) to find the probability that it will not rain and the flight will be delayed, and then we divide by P(B).
Thus, P(not A and B) = P(B) - P(A and B) = 0.11 - 0.06 = 0.05.
We now calculate the probability of it not raining given that the flight is delayed:
P(A|B) = P(not A and B) / P(B) = 0.05 / 0.11 = 0.4545.
Rounded to the nearest thousandth, P(A|B) is approximately 0.455.