Question 2.8. (MAGIC LOVERS) Mr. Plucky bought a very expensive genie lamp to ge

Question

Question 2.8. (MAGIC LOVERS) Mr. Plucky bought a very expensive genie lamp to get a correct answer to one of his personal questions. As soon as the genie appeared, Mr. Plucky questions him as to why his wife, Mrs. Plucky, remains upset with him. Mr. Plucky gave the genie the following seven options: (a) Mrs. Plucky does not like Mr. Plucky (b) Mrs. Plucky needs more money (c) Mrs. Plucky would like to buy a new car. (d) Mrs. Plucky would like to buy a new house. (e) Mrs. Plucky would like to go on a tour (f) Mrs. Plucky would like to buy new furniture. (g ) None of these. Fig. 2.9. A genie lamp Let p= 0.55 + be the probability that the genie knows the correct answer and be the probability that the genie guesses the answer. Assume that if the genie 1-p)e the guesses, the probability of giving the correct answer will be one in seven. What is the conditional probability that the genie knew the answer to Mr. Plucky's question given that the genie answered correctly? g help: Please do yourself

Explanation / Answer

P (genie knows the answer) = .55 + (DGC/(DGC+500))

= .55 + (445/945) = 1.02

This cant be possible as p has to be < 1

Please check DGC value properly. For now I will take it as 100 and solve then you can replace it

P (genie knows the answer) = .55 + (100/(100+500)) = .72

P(genie guess the answer) = 1 -P(genie knows the answer)

= 1 - .72 = .28

P(genie is right when he guess) = 1/7 * P(genie guess the answer) .. Given

= 1/7 * .28 = .04

Thus, Conditional Probability P(genie knew the answer if genie answered correctly)

= P (genie knows the answer)/ [P (genie knows the answer) + P(genie is right when he guess) ]

= .72/(.72+.04)

= .95

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