Question

The probability of having water shortages any day is 0.12.

A. In the next ten days, what is the probability that we will have water shortages in exactly two days? (10 pts)

B. What is the expected value of the number of days without water in the next ten days? (10 pts)

C. If an inspector arrives, and every day checks for water shortages, how many days on average will you have to keep your inspection if you stop when you find two days of water shortages? (10 pts)

D. What is the probability that we have to inspect entre15 and 20 days to get two days without water? (15 pts)

Answer 1

a)

probability that we will have water shortages in exactly two days =P(X=2)= =0.2330

b)

expected value of the number of days without water in the next ten days =np=10*0.12=1.2

c)

expected number of days to have 2 days of water shortage =r/p=2/0.12=16.667

d)

probability that we have to inspect entre15 and 20 days to get two days without water =P(15<=X<=20)

=P(till 14 days exactly one day water shorate and on 15th second day+till 15 days exactly one day water shorate and on 16th second day+till 16 days exactly one day water shorate and on 17th second day+..)

=

=0.0383+0.0361+0.0339+0.0317+0.0295+0.0274=0.1968