If a solar panel generates power at the rate of 400 kilowatts per day when the sky is cloudy, and 400 kilowatts per day when the sky is clear. How many kilowatts will there be per hour when it is cloudy and clear?

33.4 kW/ hr is generated when the sky is cloudy and clear.

Step-by-step explanation:

Power generated per day when the sky is cloudy = 400 kW

Power generated per day when the sky is clear = 400 kW

Power generated per hour when the sky is cloudy or clear =

Power generated per hour when the sky is cloudy and clear = 16.7 + 16.7 = 33.4 kW

a) 40% probability that San Francisco will win.

b) 80% probability that the weather was bad

Step-by-step explanation:

In this problem, there are these following probabilities:

60% probability of bad weather.

If there is bad weather, 20% probability of SF winning.

100-60 = 40% chance of good weather.

If there is good weather, 70% probability of SF winning.

(a) If they play in the Super Bowl in Wisconsin and the weatherman predicts a 60% chance of snow that day, what is the probability that San Francisco will win.

If it snows, 20% probability of winning. If it does not snow, 70% probability of winning.

0.2*0.6 + 0.7*0.4 = 0.4

40% probability that San Francisco will win.

b) Given that San Francisco lost, what is the probability that the weather was bad:

Conditional probability:

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: SF losing

Event B: Bad weather

P(A):

Probability of SF losing, which from a), is 0.6 = 60%.

P(A and B)

60% chance of snow. If it snows, 80% probability of SF losing. So

Then

80% probability that the weather was bad