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A psychologist will select 5 preschool children from a class of 11 students for awareness training....

A psychologist will select 5 preschool children from a class of 11 students for awareness training. Class has 4 boys and 7 girls. What is the probability of selecting 2 boys and 3 girls? What is the probability that sample has exactly 1 girl?

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Answer #1

Using combination for selecting sample,

nCx = n! / [ (n-x)! * x! ]

a)

P(2 boys and 3 girls) = 4C2 * 7C3 / 11C5​​​​​​​

= 6 * 35 / 462

= 0.4545

b)

P(exactly 1 girl) = 4C4 * 7C1​​​​​​​ / 11C5​​​​​​​

= 1 * 7 / 462

= 0.0152

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