(DGC value =458) Answer is provided please provide steps of the solution. Thank
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(DGC value =458) Answer is provided please provide steps of the solution. Thank you! Question 2.5. (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. SALE Fig. A genie lamp Let 07 20.CCa s0l e be the probabiliy that tegenie knows the corect answer and n2.13.., be the probability that the genie guesses the answer. Assume that 100 (2DGC+500) 100 Let 0.7 + 0.3- 2DGC+500) if the genie 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 Mi Plucky's question given that the genie answered correctly?Explanation / Answer
Here, we are given that:
P( knows correct ) = 0.7706
P( genie guesses ) = 0.2293
Also, we are given that P( correct | ginie guesses ) = 1/7
Therefore using law of total probability, we get:
P( correct ) = P( correct | ginie guesses ) P( genie guesses ) + P( knows correct ) *1
P( correct ) = (1/7)*0.2293 + 0.7706 = 0.8034
Conditional probability that the genie knew the answer to question given that the genie answered correctly is computed as:
= Probability that he knew the answer / Probability that he is correct
= 0.7706 / 0.8034
= 0.9592
Therefore 0.9592 is the required probability here.
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