SOLUTION: assume that the probability of having having a boy or a girl is 0.5 .in a family of 5 children, what is the probability that all children are boys , all the children are the same g
Question 1131173: assume that the probability of having having a boy or a girl is 0.5 .in a family of 5 children, what is the probability that all children are boys , all the children are the same gender , and there is at least one girl Found 2 solutions by rothauserc, ikleyn:Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website! use the Binomial Probability formula
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Probability (P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of success
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p = 0.5
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P (5 boys out of 5 trials) = 5C5 * (0.5)^5 * (1-0.5)^(5-5) = 1 * (0.5)^5 * 1 = 1/32 is approximately 0.03
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P (all children are same gender out of 5 trials) = 1 * (0.5)^5 * 1 = 1/32 is approximately 0.03
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P (at least 1 girl out of 5 trials) = 1 - P (there are no girls out of 5 trials) = 1 - 0.03 = 0.97
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Note "at least 1 girl" means 1 girl or 2 girls or 3 girls or 4 girls or 5 girls
: Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website! .
The correct answer to the question
what is the probability that all children are the same gender
is P(all 5 are boys) + P(all 5 are girls) = + = = .