1.Urn A has 6 white and 13 red balls. Urn B has 15 white and 3 red balls.

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1.Urn A has 6 white and 13 red balls. Urn B has 15 white and 3 red balls. We flip a fair coin. If the oucome is heads, then a ball from urn A is selected, whereas if the oucome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed heads?

2. Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1)=0.2, P(A2)=0.5,P(A3)=0.3 . If E is an event in S with P(E|A1)=0.4, P(E|A2)=0.5, P(E|A3)=0.4, compute

P(E)=

P(A1|E)=

P(A2|E)=

P(A3|E)=