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Assume that the probability that a child is a boy is 0.5. A couple has 3 children. What...

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islnds | (Level 1) Valedictorian

Posted September 18, 2013 at 10:37 PM via web

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Assume that the probability that a child is a boy is 0.5. A couple has 3 children. What is the probability that all 3 children are boys? Given that the oldest and the youngest are boys, compute the probability that all children are boys. Compute the probability that at least one child is a boy. 

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aruv | High School Teacher | (Level 2) Valedictorian

Posted September 19, 2013 at 4:31 AM (Answer #1)

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Let X  , Y , and Z represents respctively oldest , middle and youngest children.

X  is boy probabilty = .5

Y is  boy probabilty  = .5

Z is  boy probabilty  = .5

P(all boys)= .5 x .5 x .5

=1/8

(ii) when  X and Z  are boys

P( all boys )= 1/2

because  only concern probability is Y ,being boy  its probabilty will be .5

(iii) At least one boys

P(at least one boy)=1-P(all girls)

=1- .5 x .5 x.5

=1-1/8

=7/8

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