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?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! We start with the formula for binomial probabilities
P(x) = ( N! / x!(N-x)! ) * p^x * (1-p)^(N-x)
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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x=10, N=20, p=0.50
P(10) = ( 20! / 10!(20-10)! ) * (0.50)^10 * (1-0.50)^(20-10)
P(10) = 0.176197052 approx 0.18
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mean = Np = 20 * (0.50) = 10
variance = Np(1-p) = 20*(0.50)(1-0.50) = 5
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