The probability that a customer will buy a shirt is 0.4. A customer buys a tie 50% of

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naveed_786110

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The probability that a customer will buy a shirt is 0.4. A customer buys a tie 50% of the time when a shirt is
purchased, but only 10% the time when a shirt is not purchased.
Find the probability that a customer buys a tie?

Solution:

I solved it in this way.

P(Buy Shirt)=0.4 ====> P(Buy Tie) = 50%, P(NOT Buy Tie)=50%
P(Not Buy Shirt)=0.6 ===> P(Buy Tie) = 10%, P(NOT Buy Tie) = 90%

P(Buy Tie) = 0.4 * 0.5 + 0.6*0.10 = 0.26

BUT Manual says
P(Buy Tie) = 0.4 * 0.5 + 0.10 = 0.3

Whats wrong with my solution?
 
Everything in your working and reasoning looks fine to me. I think it's your manual that's wrong. I'd check with your instructor and/or the publisher of the manual. Unfortunately, in my experience, it's all too common for manuals/answer keys to be wrong.
 
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