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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.12 and the probability that the flight will be delayed is 0.18 . The probability that it will rain and the flight will be delayed is 0.09 . What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
Answer:

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is $0$ . $12$ and the probability that the flight will be delayed is $0$ . $18$ . The probability that it will rain and the flight will be delayed is $0$ . $09$ . What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth. $\newline$ Answer:

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Find probabilities using the addition rule

Full solution

Q. At LaGuardia Airport for a certain nightly flight, the probability that it will rain is

0

.

12

and the probability that the flight will be delayed is

0

.

18

. The probability that it will rain and the flight will be delayed is

0

.

09

. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.

\newline

Answer:

Denote Events: Let's denote the events as follows: $\newline$ R: It will rain. $\newline$ D: The flight will be delayed. $\newline$ We are given the following probabilities: $\newline$ $P(R) = 0.12$ (probability that it will rain) $\newline$ $P(D) = 0.18$ (probability that the flight will be delayed) $\newline$ $P(R \text{ and } D) = 0.09$ (probability that it will rain and the flight will be delayed) $\newline$ We need to find the probability that the flight would be delayed given that it is raining, which is the conditional probability $P(D|R)$ . $\newline$ The formula for conditional probability is: $\newline$ $P(D|R) = \frac{P(R \text{ and } D)}{P(R)}$
Substitute Given Values: Now we substitute the given values into the formula: $\newline$ $P(D|R) = \frac{P(R \text{ and } D)}{P(R)}$ $\newline$ $P(D|R) = \frac{0.09}{0.12}$
Perform Division: Performing the division to find $P(D|R)$ : $P(D|R) = \frac{0.09}{0.12}$ $P(D|R) = 0.75$
Round the Answer: We need to round the answer to the nearest thousandth as instructed: $P(D|R) \approx 0.750$

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