Home > Probability
| Black Jack (Posted on 2005-03-17) |
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Jack owns many black shirts and pants. However, Jack gets up late each day, and as a result, he just chooses his clothes at random.
He would like to have at least one black item on and he knows there is a .16 chance just his shirt will be black, there is a .27 chance just his pants will be black, and there is a chance less than both of these he won't have anything black on.
If the color of his shirt and pants are independent of each other, what is the chance both are black?
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Submitted by Gamer
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Rating: 3.0000 (2 votes)
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Solution:
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If p is the probability that both will be black, an equation can be written because black shirt and black pants are independent.
(.16+p)(.27+p)=p
.0432+.43p+p^2=p
p^2-.57p+.0432=0
(p-.48)(p-.09)=0
Because 1-(.16+.27+.48)=.9 and is less than both .16 and .27, there is a .48 chance he will have both a black shirt and black pants on. |
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