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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.08 . The probability that it will not rain and the flight will leave on time is 0.78 . What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
Answer:

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is $0$ . $19$ and the probability that the flight will be delayed is $0$ . $08$ . The probability that it will not rain and the flight will leave on time is $0$ . $78$ . What is the probability that the flight would leave on time when it is not 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

.

19

and the probability that the flight will be delayed is

0

.

08

. The probability that it will not rain and the flight will leave on time is

0

.

78

. What is the probability that the flight would leave on time when it is not 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. $\newline$ \(\newlineeg R\): It will not rain. $\newline$ \(\newlineeg D\): The flight will leave on time. $\newline$ We are given the following probabilities: $\newline$ $P(R) = 0.19$ $\newline$ $P(D) = 0.08$ $\newline$ P(\(\newlineeg R \text{ and } $\newline$ eg D) = 0.78\) $\newline$ We need to find the probability that the flight leaves on time given that it is not raining, which is P(\(\newlineeg D \,|\, $\newline$ eg R)\).
Find P(\(\newlineeg R)\): First, we need to find the probability that it is not raining, which is P(\(\newlineeg R)\). This is the complement of the probability that it will rain. $P( eg R) = 1 - P(R)$ $P( eg R) = 1 - 0.19$ $P( eg R) = 0.81$
Calculate P(\(\newlineeg D | $\newline$ eg R)\): Now, we use the definition of conditional probability to find P(\(\newlineeg D | $\newline$ eg R)\). The formula for conditional probability is: $\newline$ $P( eg D | eg R) = \frac{P( eg D \text{ and } eg R)}{P( eg R)}$ $\newline$ We already have P(\(\newlineeg D \text{ and } $\newline$ eg R) = 0.78\) and P(\(\newlineeg R) = 0.81\).
Substitute and Solve: Substitute the values into the formula to find P(\(\newlineeg D | $\newline$ eg R)\): $P( eg D | eg R) = \frac{0.78}{0.81}$ $P( eg D | eg R) \approx 0.963$

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