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If there is an 80% chance of rain and a 50% chance of wind and rain, what is the probability that it is windy, given that it is rainy? Round your answer to the nearest percent.

Verified Answer :

lulu1991

The total probability when given it is rainy is 80%. Among them, the windy probability among 80% is 50%. So the total probability is 50%/80%=62.5%≈63%.

Answer:

The probability that it is windy, given that it is rainy is:

                             62.5%≈63%

Step-by-step explanation:

Let A denote the event that it will rain.

B denote the event that it is windy.

A∩B denote the event that it is rainy and windy.

Let P denote the probability of an event.

i.e. we have:

P(A)=0.80

( Since there are 80% chance of rain)

P(A∩B)=0.50

(Since there are 50% chance of wind and rain)

We are asked to find:

P(B|A)

We know that:

\(P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(B|A)=\dfrac{0.50}{0.80}\\\\\\P(B|A)=0.625\)

Hence, the probability in percent is:

                   62.5%≈63%

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