document.write( "Question 1011689: 10. A coin is tossed 20 times, what’s the probability of getting exactly 10 heads? What is the variance and the mean? \n" ); document.write( "

Algebra.Com's Answer #627426 by rothauserc(4718) $\"\"$ $\"About$

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We start with the formula for binomial probabilities
\n" ); document.write( "P(x) = ( N! / x!(N-x)! ) * p^x * (1-p)^(N-x)
\n" ); document.write( "where P(x) is the probability of x successes out of N trials, N is the number of trials, and p is the probability of success on a given trial. Applying this to our problem
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\n" ); document.write( "x=10, N=20, p=0.50
\n" ); document.write( "P(10) = ( 20! / 10!(20-10)! ) * (0.50)^10 * (1-0.50)^(20-10)
\n" ); document.write( "P(10) = 0.176197052 approx 0.18
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\n" ); document.write( "mean = Np = 20 * (0.50) = 10
\n" ); document.write( "variance = Np(1-p) = 20*(0.50)(1-0.50) = 5
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