Question

in july in virginia, the temperature can quickly rise above 90 degrees fahrenheit, which can also lead to thunderstorms. the probability that the temperature will rise above 90 on a randomly chosen day is 0.68, and the probability of thunderstorms is 0.29. if the temperature rises above 90 degrees, the probability of a thunderstorm is 0.56. what is the probability that the temperature rises above 90 degrees and there is a thunderstorm on a randomly chosen day in july? 0.16 0.20 0.29 0.38

Explanation:

Step1: Define events

Let \(A\) be the event that the temperature rises above 90 degrees, \(P(A)=0.68\). Let \(B\) be the event of thunderstorms, \(P(B) = 0.29\). The conditional probability \(P(B|A)=0.56\).

Step2: Use the formula for conditional probability

The formula for conditional probability is \(P(B|A)=\frac{P(A\cap B)}{P(A)}\).
Rearrange it to find \(P(A\cap B)\): \(P(A\cap B)=P(B|A)\times P(A)\).

Step3: Calculate the probability

Substitute the values: \(P(A\cap B)=0.56\times0.68 = 0.3808\approx0.38\)

Answer:

0.38