The first date went well. You are still dating the same person and still looking

Question

The first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now? A. 0.41 B. 0.23 C. 0.28 D. 0.1 E. 0

Explanation / Answer

Is this the same problem where the probability of a great match is 0.1? If so, the solution is:

Let

A = kind to animals
M = great match

Thus, as

P(M|A) = P(M) P(A|M) / P(A)

As

P(A) = P(M) P(A|M)+ P(M) P(A|M) = 0.1*0.9 + (1-0.1)*0.7 = 0.72

Then

P(M|A) = P(M) P(A|M) / P(A) = 0.1*0.9/0.72 = 0.125 [ANSWER. The closest is D. Is the probability of a great match still 0.1?]

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