In Montana, the probability it will snow tomorrow is .55. The weather forecast correctly says that...

In Montana, the probability it will snow tomorrow is .55. The weather forecast correctly says that it will snow tomorrow when it will actually snow tomorrow with probability .9. The weather forecast also correctly predicts it will not snow tomorrow when it actually will not snow tomorrow with probability .95. Use a tree diagram to calculate the following questions:

What is the probability that the weather forecast says that it will snow tomorrow AND it actually will snow tomorrow?

What is the probability that the weather forecast says that it will snow tomorrow?

What the probability that it will snow tomorrow in Montana, given that the weather forecast says it will snow tomorrow.

What the probability that it will NOT snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow.

What the probability that it will snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow.

Solutions

Expert Solution

a) the probability that the weather forecast says that it will snow tomorrow AND it actually will snow tomorrow = 0.9*0.55 = 0.495

b) the probability that the weather forecast says that it will snow tomorrow = 0.9*0.55+0.05*0.45 = 0.5175

c) the probability that it will snow tomorrow in Montana, given that the weather forecast says it will snow tomorrow = 0.495/0.5175 = 0.9565

d) the probability that it will NOT snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow = ( 0.95*0.45)/(0.95*0.45+0.55*0.1) = 0.886

e) the probability that it will snow tomorrow in Montana, given that the weather forecast says it will NOT snow tomorrow = 0.1*0.55/(0.1*0.55+0.95*0.45) = 0.114

orchestra answered 1 year ago

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