Due to recent energy crisis in California, rolling blackouts were necessary and more might be necessary in the future. Assume that there is a 60% chance that the temperature will exceed 85 degrees Fahrenheit on any given day in July in a particular area. Assume that there is a 30% chance that a rolling blackout will be needed in that area. There is a 20% chance that both events will occur. Find the probability that the temperature will exceed 85 degrees Fahrenheit on a given July day but that no rolling blackout will be needed on that day.

Step-by-step explanation:

Define the events,

A. The temperature will exceed 85°F on a given july day.

B. The rolling blackout will be needed on that day.

From the given information, there is 60% chance that the temperature will exceed 85°F on any given july day in a particular area. That is P (A) = 0.60, that 30% chance that a rolling blackout will be needed in that area. That is P (B) = 0.30, and the 20% chance that both events will occur. That is P (A∩B) = 0.20

Therefore, the probability that the temperature will exceed 85°F on a given july day but that no rolling blackout will be needed on that day is.

P (A∩B') = P (A) - P (A∩B) = 0.60-0.20=0.40

Thus, th probability that the temperature will exceed 85°F on a given july day but that no rolling blackout will be needed on that day is 0.40

The probability of the temperature exceeding 65 degrees Fahreneit but not needing a rolling blackout is 0.4 - Hence, there is a 40% chance.

Step-by-step explanation:

Lets call F the event 'the temperature will exceed 85 degrees Fahrenheit' and B the event 'a blackout will be needed'.

We want P (F ∩ B^c), note that if F happens, there could be 2 disjoint possible events: B or B^c, hence

P (F) = P (F ∩ B) + P (F ∩ B^c)

Hence

P (F ∩ B^c) = P (F) - P (F ∩ B) = 0.6 - 0.2 = 0.4