document.write( "Question 481883: If a family has 3 children, find the probability that there is at least 1 boy among the children \n" ); document.write( "

Algebra.Com's Answer #329941 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "This depends on what you consider the probability of a male child on any given trial. If you are just wanting to do an exercise in calculating a binomial distribution, then you can use 50% as the probabiltiy of a boy on any give trial. I reality, it doesn't actually work out that way. See:\r
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\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\">Gender Odds\r
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\n" ); document.write( "\n" ); document.write( "And note that the odds of a girl after having had one or two boys, (or vice versa) varies at each instance of a trial.\r
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\n" ); document.write( "\n" ); document.write( "If you just need the binomial distribution on a 50/50 per trial basis, then you can either calculate the probability of exactly 1 boy, exactly 2 boys, and exactly 3 boys, then sum the three probabilities, or you can calculate the probability of exactly 3 girls (same as exactly 3 boys) and subtract from 1. That's because the only way you can't have at least 1 boy is to have all three girls.\r
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\n" ); document.write( "\n" ); document.write( "The probability of

successes in

trials where

is the probability of success on any given trial is given by:\r
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\n" ); document.write( "\n" ); document.write( "Where

is the number of combinations of

things taken

at a time and is calculated by

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\n" ); document.write( "\n" ); document.write( "For your problem,

, and

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\n" ); document.write( "\n" ); document.write( "So:\r
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\n" ); document.write( "\n" ); document.write( "Note that

\ 0\ \in\ \mathbb{Z}\"> and

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\n" ); document.write( "\n" ); document.write( "Next time, flip a coin. You get the same 50/50 results, but each experiment is a good deal less messy and time consuming compared to having babies.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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