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Answer only 8.15, do not answer 8.14. If all work is shown, I will thumbs up.*8.14 The probability of a boy being born equals.50, or 1/,, as does the probability of a girl being born. For a randomly sel

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Answer #1

Let X be an event that a boy is born

X is a binomial random variable where

n = 3, p = 0.5

We know that, probability of binomial distribution is given by

P(X=x) = (m.) * p* * (1 – p)(n-1) , x = 0,1,2,3

(a)

The required probability = P(X = 3) = 0.125

(b)

The required probability = P(X = 0) = 0.125

(c)

The required probability = P(X = 0 or X = 3)

= P(X = 0) + P(X = 3)

= 0.125 + 0.125

= 0.25

(d)

The probability of neither 3 boys or 3 girls is,

= 1- (probability of 3 boys + probability of 3 girls)

= 1 - {P(X = 0) + P(X = 3)}

= 0.75

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