Question

Paragraph Styles =0.42*0.24/0.35 =0.288 =28.8% 5. Dr. Foster remembers to take his umbrella with him 80% of the days. It rains on 30% of the days when he remembers to take his umbrella, and it rains on 60% of the days! when he forgets to take his umbrella. What is the probability that he remembers his umbrella when it rains? I

Answer 1

Let U represents the event that he takes his umbrella.

Let R represent the event that it rains.

Then we have:

P(U) = 0.80

P(U') = 1-P(U) = 1-0.80=0.20

P(R/U) = 0.30

P(R/U') = 0.60

We need to find the probability that: P(U/R)

Using Baye's theorem:

$P(U/R) = \frac{P(R/U)*P(U)}{P(R/U)*P(U)+P(R/U')*P(U')}$

$\rightarrow P(U/R) = \frac{0.30*0.80}{0.30*0.80+0.60*0.20}$

$\rightarrow P(U/R) = 0.666666667$

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