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Probability

Question

Wired Faculty App

Eight coins are thrown simultaneously. Find the probability of getting at least six heads.

Solution

Let p denote the probability of getting a head and q the probability of not getting a head, then

straight p space equals 1 half comma space space space straight q space equals space 1 half

∴ probability of getting at least six heads when 8 coins are thrown simultaneously
= P(6) + P(7) + P(8)

equals space straight C presuperscript 8 subscript 6 space open parentheses 1 half close parentheses to the power of 6 space open parentheses 1 half close parentheses squared space plus space straight C presuperscript 8 subscript 7 space open parentheses 1 half close parentheses to the power of 7 space open parentheses 1 half close parentheses space plus space straight C presuperscript 8 subscript 8 space open parentheses 1 half close parentheses to the power of 8 equals space open parentheses 1 half close parentheses to the power of 8 space open square brackets straight C presuperscript 8 subscript 6 space plus space straight C presuperscript 8 subscript 7 space plus space straight C presuperscript 8 subscript 8 close square brackets equals space 1 over 256 open square brackets fraction numerator 8 space cross times space 7 over denominator 1 space cross times 2 end fraction plus space 8 over 1 plus 1 close square brackets space equals 1 over 256 left square bracket 28 plus 8 plus 1 right square bracket space equals 37 over 256.

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