11. (12 points) Refer to the Venn Diagram for events A and B. Note that the set has 90 elements. a) P(A\cup B)= b) P((A\cup B)') = c) P(A|B)= Recall: P(A|B) = \frac{P(A\cap B)}{P(B)} 12. The chances of Ahmed wearing his lucky socks is 25%. When he does wear his lucky socks, the Bucks have a 65% chance of winning. When he does not wear his lucky socks, the Bucks have a 20% chance of winning. Let S = "wears lucky socks", and let W = "Bucks win" a) Fill in the tree with the given information. b) Use Bayes' Formula to find the probability that Ahmed wore his lucky socks given that the Bucks won. That is, find P(S|W) = \frac{product\ of\ paths\ leading\ to\ W\ through\ S}{sum\ of\ all\ branch\ products\ leading\ to\ W} Answer:
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Since we have a Venn diagram with 90 elements, we can use the formula P(AUB) = P(A) + P(B) - P(A∩B). However, we are not given the individual probabilities of A and B or the probability of their intersection, so we cannot calculate P(AUB) at this time. Show more…
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