As an extreme weather adjustment an electrical supply compan

As an extreme weather adjustment, an electrical supply company provides a lower supply rate to households that use less than 500 kwh per month during summer months. 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) = 0.20, P(A) = 0.22, and P(J ? A) = 0.10. What is the probability that the household gets the low rate in either July, August, or both?

Find the probability that the household gets the low rate in neither July nor August and find the probability that the household gets the low rate in July but not in August.

Solution

P(J)=0.20

P(A) = 0.22

P(July and Aug) = 0.10 (given)

P(either in July or in August or both) = P(July)+P(August)-P(BOth)

= 0.20+0.22-0.10

= 0.32