# Probability with unlimited numbers

• February 11th 2010, 07:43 AM
lph2
Probability with unlimited numbers
Heres the question,
A store carries sweaters in three colors (Brown, gray and red). Assume he store has an unlimited number of sweaters and that customers select color at random.

a. What is the probability that three customers will select the same color?

b. Determine the probability the three customers will not all select the same color.

Thanks in advance for any help.
• February 11th 2010, 08:25 AM
Plato
Quote:

Originally Posted by lph2
Heres the question,
A store carries sweaters in three colors (Brown, gray and red). Assume he store has an unlimited number of sweaters and that customers select color at random.
a. What is the probability that three customers will select the same color?
b. Determine the probability the three customers will not all select the same color.

This is an ill formed question. If seven or more customers buy sweaters then three of them will necessarily buy the same color. Is that what the question really says?
• February 11th 2010, 08:52 AM
lph2
Quote:

Originally Posted by Plato
This is an ill formed question. If seven or more customers buy sweaters then three of them will necessarily buy the same color. Is that what the question really says?

No there are an unlimited number of each color sweaters and only three people picking sweaters. Basically the problem says you do not have to subtract 1 from the denominator to make up for the missing colored sweater. I thought the probability would be 1/3 cubed for the first question but that does not seem to make sense to me. Let me know if this helps
• February 11th 2010, 09:32 AM
Plato
Quote:

Originally Posted by lph2
No there are an unlimited number of each color sweaters and only three people picking sweaters. Basically the problem says you do not have to subtract 1 from the denominator to make up for the missing colored sweater. I thought the probability would be 1/3 cubed for the first question but that does not seem to make sense to me. Let me know if this helps

There are $3^3=27$ for the three people to buy a sweater.
There are just 3 ways for the three people to all buy the same color.