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[PR] Problem on Probability

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[PR] Problem on Probability

by Xia_devil » Tue Jun 24, 2008 2:04 am
Hey guys

How do i solve this problem ?

A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?
Last edited by Xia_devil on Tue Jun 24, 2008 2:50 am, edited 1 time in total.
With regards,
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by atlantic » Tue Jun 24, 2008 2:49 am
Hi xia_devil,

Answer is 1/42. Post calculation if correct.
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Re: [PR] Problem on Probability

by Motherjane » Tue Jun 24, 2008 3:45 am
Xia_devil wrote:Hey guys

How do i solve this problem ?

A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?
The answer is 1/81.

Here's how I went abt it.

First day selection - (3C1/3) * (2C1/2) * (3C1/3) = 1
Second day selection - (2C1/3) * (1/2) * (2C1/3) = 2/9
Third day selection - (1/3) * (1/2) * (1/3) = 1/18

Probability - 1*2/9*1/18 = 1/81 = (1/3) ^ 4
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by atlantic » Tue Jun 24, 2008 5:26 am
Motherjane,

You're right. Again a mistake in my calculation.

Day 1: 1 (because you can pick anything)
Day 2: 1/2 (for the shoes) * 2/3 (for the shirts) * 2/3 (for the pants)
Day 3: 1/2 (for the shoes) * 1/3 (for the shirts) * 1/3 (for the pants)

Then 1*1/2*2/3*2/3*1/2*1/3*1/3= 4/324=1/81.
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