You have arranged to go camping for two days in March.You believe that the probability that it will rain on the first day is 0.5.If it rains on the first day,the probability that it also rains on the second day is 0.7.If it doesn't rain on the first day,the probability that it rains on the second day is 0.2.Let the random variable X be the number of rainy days during your camping trip.Find the expected value of X.
A)μ = 1.05
B)μ = 0.85
C)μ = 1.2
D)μ = 0.95
E)μ = 0.8

Question

Quizplus · Accepted Answer

We can use the formula for expected value:

E(X) = ΣxP(X=x)

where x is the number of rainy days during the camping trip.

There are three possible scenarios:

1) It rains on the first day and second day: P(X=2) = 0.5 * 0.7 = 0.35
2) It rains on the first day but not on the second day: P(X=1) = 0.5 * (1-0.7) = 0.15
3) It doesn't rain on the first day but rains on the second day: P(X=1) = (1-0.5) * 0.2 = 0.1
4) It doesn't rain on either day: P(X=0) = (1-0.5) * (1-0.2) = 0.4

Therefore, E(X) = 2*0.35 + 1*0.15 + 1*0.1 + 0*0.4 = 0.95

Therefore, the answer is D) μ = 0.95.

You Have Arranged to Go Camping for Two Days in March.You