The first date went well You are still dating the same perso

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

Solution

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?]