Dgc:492 SC: 492 Exercise 3.6. (SAVE WATER FOR FUTURE) As a conservative measure,

Question

Dgc:492 SC: 492 Exercise 3.6. (SAVE WATER FOR FUTURE) As a conservative measure, a water company provides a ouseholds that use less than 10,000 gallons per month. Let J denote the low rate to event that a household gets the low rate in July, and let A denote the event that the same household gets the low rate in August. Suppose: DGC+500 1,0 9 DOC+200 = Fig. 3.6. Raining and (Door." (DGC +400)2 0.042 … (a ) Find the probability that the household gets the low rate in either July, August or both. (b) Find the probability that the household gets the low rate in neither July nor August. (c) Find the probability that the household gets the low rate in July but not in August

Explanation / Answer

a)

P(J U A) = 0.4959 +0.7109 - 0.3042 = 0.9026

b)

we know that

neither A nor B = not(A or B)
P(A or B)' = 1 - P(A or B)
= 1 - [P(A) + P(B) - P(A and B)]

1- 0.4959 - 0.7109 +0.3042 = 0.0974

c)
p july but not august

P(J) = 0.4959
P(not A) = 1 - P(A) = 1 - 0.7109 = 0.2891

so the required probability is
0.4959*0.2891 = 0.1433

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