Exercise 3.6. (SAVE WATER FOR FUTURE) As a conservative measure, a water company

Question

Exercise 3.6. (SAVE WATER FOR FUTURE) As a conservative measure, a water company provides a low rate to households that use less than 10,000 gallons per month. Let J denote the 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: P(J) = DGC+500 P(A) = DOG+200 Fig. 3.6. Raining and (DGC+400) (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

Pj = 441/(441+500) = 0.468
PA = 441/(441+200) = 0.687
P(A intersect J) = ((441)^2)/(881)^2 = 0.250

a)

P(J U A) = 0.468 +0.687 - 0.250 = 0.905

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- 0.468 - 0.687 +0.250 = 0.095

c)
p july but not august

P(J) = 0.468
P(not A) = 1 - P(A) = 1 - 0.687 = 0.313

so the required probability is
0.468*0.313 = 0.1464

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