Question

You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during the festival, but the weather forecast says there is a 15% chance of rain on the first day, a 10% chance of rain on the second day, a 20% chance of rain on the third day, a 20% chance of rain on the fourth day, and a 60% chance of rain on the fifth day. Assume these probabilities are independent of whether it rained on the previous day or not. What is the probability that it does not rain during the entire festival

Answer 1

Answer:

Probability that it does not rain during the entire festival = 0.19584

Step-by-step explanation:

We are given that you and a group of friends are going to a five-day outdoor music festival during spring break.

Also, Probability that there may be rain on first day, P(A) = 0.15

Probability that there may be rain on second day, P(B) = 0.10

Probability that there may be rain on third day, P(C) = 0.20

Probability that there may be rain on fourth day, P(D) = 0.20

Probability that there may be rain on fifth day, P(E) = 0.60

It is also provided that these probabilities are independent of whether it rained on the previous day or not.

Now, probability that it does not rain during the entire festival = Probability that there may not be rain on all five days

= (1 - P(A)) $\times$ (1 - P(B)) $\times$ (1 - P(C)) $\times$ (1 - P(D)) $\times$ (1 - P(E))

= (1 - 0.15) $\times$ (1 - 0.10) $\times$ (1 - 0.20) $\times$ (1 - 0.20) $\times$ (1 - 0.60)

= 0.85 $\times$ 0.90 $\times$ 0.80 $\times$ 0.80 $\times$ 0.40 = 0.19584