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If boys and girls are equally likely to be born, what is the probability that in a randomly selected family of $4$ children, there will be at least one boy? (Find the answer using a formula. Round your answer to three decimal places.) What formula are they talking about?

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$P(x \geq 1) = 1 - P(x < 1) = 1 - P(x = 0) = 1 - .5^4 = 1 - 0.0625 = 0.9375$

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  • $\begingroup$ What if it were 7 children instead of 4? Would the answer be .992? $\endgroup$ – Kevin Oct 15 '14 at 4:47
  • $\begingroup$ then you have: $1 - 0.5^7$ $\endgroup$ – DeepSea Oct 15 '14 at 4:49
  • $\begingroup$ One-third of a certain breed of rabbits are born with long hair. What is the probability that in a litter of 10 rabbits, exactly 7 will have long hair? (Find the answer by using a formula. Round your answer to three decimal places.) What formula would you use for this? $\endgroup$ – Kevin Oct 15 '14 at 4:51
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    $\begingroup$ @Kevin that is a separate question. Ask that separately. $\endgroup$ – M.S.E Oct 15 '14 at 4:53
  • $\begingroup$ $p = 1/3$, $q = 2/3$, $n = 10$, $k = 7$, use $P(x = k) = \binom{n}{k}p^kq^{n-k}$ $\endgroup$ – DeepSea Oct 15 '14 at 4:54

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