SOLUTION: Cathy owns a collection of 25 ballpoint pens of which 6 are pilot. If 2 ballpoints are selected at random, find the probability that both are made by pilot.

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Question 1202678: Cathy owns a collection of 25 ballpoint pens of which 6 are pilot. If 2 ballpoints are selected at random, find the probability that both are made by pilot.
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342) About Me  (Show Source):
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there are 6 pilot pens out of a total of 25.
the proability of getting a pilot on the first draw is 6/25.
after you draw the pilot, there are 5 pilots left out of a total of 24.
the probability of getting a pilot on the second draw is 5/24.
the probability of getting a pilot on the first draw and a pilot on the second dra w is 6/25 * 5/24 = 30/600 = 3/60 = 1/20.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Cathy owns a collection of 25 ballpoint pens of which 6 are pilot.
If 2 ballpoints are selected at random, find the probability that both are made by pilot.
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The probability that the first ballpoint is pilot equals 6%2F25.

The probability that the second ballpoint is pilot equals 5%2F24.


The probability that both ballpoints are pilot is the product

    %286%2F25%29%2A%285%2F24%29 = reduce fractions = %286%2F5%29%2A%281%2F24%29 = reduce fraction again = %281%2F5%29%2A%281%2F4%29 = 1%2F20 = 0.05 = 5%.    ANSWER

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The two responses you have already received both use an elementary method for finding the answer.

That is one of two basic methods for solving problems like this. For more complicated similar problems, you will usually want to know the second basic method.

We are choosing 2 of the 6 pens that are made by pilot and 0 of the other 19 pens.

The total number of ways of choosing 2 of the 25 pens is C(25,2).

The number of ways of choosing 2 of the 6 pilot pens and none of the other 19 pens is C(6,2)*C(19,0).

The probability of choosing 2 of the 6 pilot pens is

%28C%286%2C2%29%2AC%2819%2C0%29%29%2FC%2825%2C2%29=15%2F300=1%2F20

ANSWER: 1/20