document.write( "Question 1082679: Find the probability that in a pig family of 4 offspring there will be at least 1 male and 1 female offspring?. Assume that the probability of a male offspring is 0.5 \n" ); document.write( "

Algebra.Com's Answer #696750 by natolino_2017(77) $\"\"$ $\"About$

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instead of finding the working scenario, let's find the not working scenarios.\r
\n" ); document.write( "\n" ); document.write( "we have two: (all the offspring are male) or (all the offspring are female)\r
\n" ); document.write( "\n" ); document.write( "Also every offspring is independet from the rest.\r
\n" ); document.write( "\n" ); document.write( "P(All the offspring are male) =(1/2)^4 = 1/16.\r
\n" ); document.write( "\n" ); document.write( "P(All the offspring are female) =(1/2)^4 = 1/16.\r
\n" ); document.write( "\n" ); document.write( "Using the complement\r
\n" ); document.write( "\n" ); document.write( "P() = 1 - (1/16+ 1/16) = 7/8.\r
\n" ); document.write( "\n" ); document.write( "Another way is counting all the possible scenarios:\r
\n" ); document.write( "\n" ); document.write( "every birth has two options, so total cases are = 2*2*2*2 = 2^4 = 16.\r
\n" ); document.write( "\n" ); document.write( "So the working cases are 16 - 2 = 14.\r
\n" ); document.write( "\n" ); document.write( "P() = (working cases) / (all cases) = 14/16 = 7/8.\r
\n" ); document.write( "\n" ); document.write( "Obs: do not confuse counting the cases with the calculus of the probabilities, the first way operates with probabilities, the second operates with cases and then calculates the probability.\r
\n" ); document.write( "\n" ); document.write( "@natolino_ \r
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