MHB Probability question where an object is chosen randomly out of two objects

[tantrik]

Dear friends,

I am stuck at the following probability problem. Will appreciate your help.

Two opera singers, Mario and Clarissa both perform on the same night, in separate recitals. The independent probabilities that two newspapers X and Y publish reviews of their recitals are given below:

Probability of review in newspaper X
================================ ====
Mario's recital - 1/2
Clarissa's recital - 2/3

Probability of review in newspaper Y
================================ ====
Mario's recital - 1/4
Clarissa's recital - 2/5

Mario buys one of the newspapers at random. What is the probability that it has reviewed "both" recitals?

I did this way: P(reviewed both recitals) = P(buys paper X)*P(X reviews Mario)*P(X reviews Clarissa) = (1/2)*(1/2)*(2/3) = 1/6

But 1/6 is not the correct answer. Let me know where I am wrong and why.

Thanks in advance.

 

[HallsofIvy]

Your answer is wrong because it refers only to newspaper X! You calculated "the probability that she bought newspaper X and both were reviewed". If she had bought newspaper Y then the probability both are reviewed is (1/4)(2/5)= 1/10. The probability she bought newspaper Y was 1/2 so the probability she bought newspaper Y and both were reviewed is (1/2)(1/10)= 1/20. The probability both were reviewed in whatever paper she bought is the sum: 1/20+ 1/6= 3/60+ 10/60= 13/60.

 

[tantrik]

Your answer is wrong because it refers only to newspaper X! You calculated "the probability that she bought newspaper X and both were reviewed". If she had bought newspaper Y then the probability both are reviewed is (1/4)(2/5)= 1/10. The probability she bought newspaper Y was 1/2 so the probability she bought newspaper Y and both were reviewed is (1/2)(1/10)= 1/20. The probability both were reviewed in whatever paper she bought is the sum: 1/20+ 1/6= 3/60+ 10/60= 13/60.

Thanks for the solution. Now I understand where the mistake was.