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webwork i matho pring19mcnelis / hw4 binomial random variables / 1 HW4 Binomial Random Variables: Problem 1 Previous Problem Problem List Next Problem (1 point) In a family with 5 children, excluding multiple births, what is the probability of having exacty 1 girt? Assume that having a boy is as likely as having a girl at each birth. Preview My Answers Submit Answers

Answer 1

Define a random variable X=number of girl child's in the family of 5

Then P(exactly one girl child)=P(X=1)

Now having exactly one girl child in the family= family having 4 boy child and one girl child considering all orders of birth of boy and girl child

Now 4 boys and one girl out of 5 can be selected in 5!/(4!*1!)=5 ways.

Again the probability of having 4 boy child and one girl child in the family in a specified birth order is (.5)^4*(.5), as having a boy child and a girl child are equally likely , that is, occurs with probability .5.

Then P(X=1)=5*(.5)^4*(.5)=5/32