Probability Question from Princeton Online Review

by **Guest** Fri Aug 01, 2008 1:46 pm

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 (1/3) to the power 4

by RA Sat Aug 02, 2008 8:02 am

On day 1 the man could choose any combination of the outfit and therefore the probablity is 1

On day 2 the probabilities are as follows:
2/3 (probability of picking a different shirt)
2/3 (probability of picking a different pair of pants )
1/2 (probability of picking the same pair of shoes)

On day 3 the probabilities are as follows:
1/3 (probability of picking a different shirt)
1/3 (probability of picking a different pair of pants )
1/2 (probability of picking the same pair of shoes)

Total Probability = (Day 1 Probability) * (Day 2 Probability) * (Day 3 Probability)
= (1 * 1* 1) * (2/3 * 2/3 * 1/2) * (1/3 * 1/3 * 1/2) = (1/3)^4

Hope that helps

by **Guest** Mon Aug 04, 2008 12:44 pm

Hi,
thanks for the reply.

by **RonPurewal** Wed Oct 29, 2008 7:42 am

RA Wrote:On day 1 the man could choose any combination of the outfit and therefore the probablity is 1

On day 2 the probabilities are as follows:
2/3 (probability of picking a different shirt)
2/3 (probability of picking a different pair of pants )
1/2 (probability of picking the same pair of shoes)

On day 3 the probabilities are as follows:
1/3 (probability of picking a different shirt)
1/3 (probability of picking a different pair of pants )
1/2 (probability of picking the same pair of shoes)

Total Probability = (Day 1 Probability) * (Day 2 Probability) * (Day 3 Probability)
= (1 * 1* 1) * (2/3 * 2/3 * 1/2) * (1/3 * 1/3 * 1/2) = (1/3)^4

Hope that helps

well played.