Question

PLEASE MAKE CLEAR STEPS.

The probability of having shortages of water on any given day is 0.12.

a. In the next ten days, what is the probability that we have water shortages in exactly two days?

b. What is the expected value of the number of days without water in the next ten days?

c. If an inspector arrives, and every day checks for water shortages, how many days on average will he have to maintain his inspection if he stops when he finds two days with water shortages?

d. What is the probability that we have to inspect between 15 and 20 days to get two days without water?

PLEASE MAKE CLEAR STEPS.

Answer 1

Here, we are given that: P( shortage ) = 0.12

a) The probability here is computed using the binomial probability function as:

Therefore 0.2330 is the required probability here.

b) The expected number of days for water shortage here is computed as:

E(X) = np = 10*0.12 = 1.2

Therefore 1.2 days is the expected number of days here.

c) For fiding 2 days of water shortages, the expected number of days he needs to check could be computed here as:

d) Now the probability that we have to inspect between 15 and 20 days to get two days without water is computed here as:

= Probability that it takes 16, 17, 18 or 19 days

Therefore 0.1311 is the required probability here.