For the problems where you need to find the probability of a

For the problems where you need to find the probability of an event (that\'s problems 3 through 8) give the Experiment, the Sample space, the Event space and then calculate the probabilities. Simplify your answers as much as possible until you obtain a reduced fraction rather than a decimal number (for example, give the answer as rather than 0.236).

Solution

A day has to be either rainy or sunny hence two outcomes

Sample space is

rain is predicted and rain           Rain is predicted no rain

Sunny if predicted not sunny       sunny is predicted and sunny

a) Prob rain predicted = Prob fo rain predicted and rain + Prob rain predicted and no rain

= 0.90(0.05) + 0.04(0.10)

= 0.045 + 0.04 = 0.085

b) Prob that it rain when he predicts tain = 0.90(0.05) = 0.045