Question 1048797: 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
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Mario's recital - 1/2
Clarissa's recital - 2/3
Probability of review in newspaper Y
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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.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
P(X reviews both) = (1/2)(2/3) = 1/3
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Probability of review in newspaper Y
====================================
Mario's recital - 1/4
Clarissa's recital - 2/5
P(Y reviews both) = (1/4)(2/5) = 1/10
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Mario buys one of the newspapers at random. What is the probability that it has reviewed "both" recitals?
P(reviewed both | bought X) + P(reviewed both | bought Y)
(1/2)(1/3) + (1/2)(1/10) = 1/6 + 1/20 = (26/120) = 0.217
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Cheers,
Stan H.
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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.
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Looks like you were on the right path.
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