SOLUTION: There is a committee of 4 people. There are 5 teachers and 20 parents to choose for this committee. What is the probability that: A: All are teachers? B: Two are teachers and two

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Hi,
*Note: The probability of x successes in n trials is:
.
P = nCx* * where p and q are the probabilities of success and failure respectively.
.
nCx =
.
Question states p(teacher drawn) = 5/25 0r .2 and q = .8
.
A.
4C4 =
.
P(4 teachers are selected) = = .0016
.
B.
4C2 =
.
P(2 teachers and 2 parents) =

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No. of ways to choose 4 people from total 25 people = 25C4
(i.e no. of sample space)
A:
No. of ways to choose 4 people from 5 teachers = 5C4
probability of all 4 are teachers = no. of favourable event/ no. of sample space

= 5C4 / 25C4

= 5 / 12650

= 1 / 2530

..............................................................................
B.
No. of ways to choose 2 teachers and 2 parents = 5C2 * 20C2

= 10 * 190 = 1900

probability of 2 teachers and 2 parents = 1900 / 25C4

= 38 / 253


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