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Help in this Probability Question ASAP!?

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A COMMITTEE OF 5 PEOPLE IS TO BE FORMED FROM 15 PARENTS AND 10 teachers. Find the probability that the committee will consist of at least one parent.

asked Jul 11, 2014 in PRECALCULUS by anonymous

1 Answer

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If there are n items, and want to choose k of them, then number of combinations are nCk = n! / (n-k)! k!.
From the 10 teachers, pick a committee of 5 members → 10C5

= 10! / (10 - 5)! 5! =

10! / 5! 5!

= 252 ways.
The total ways could make a committee from any of the 25(15 + 10) people → 10C5

= 25! / (25 - 5)! 5!

= 25! / 20! 5!

= 53,130 ways.

Probability of no parent (Pno parent) = 10C5/25C5

= 252/53130

= 6/1265.

Probability of at least one parent = 1 - Pno parent.
= 1 - 6/1265
= 1 - 0.004743

= 0.9952.

The probability that the committee will consist of at least one parent is 0.9952.

answered Jul 11, 2014 by lilly Expert

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