A fair coin is tossed 7 times. Find the probability of obtaining at least 5 tails.

Solution

Here n = 7
Let p be the probability of getting a tail
$therefore space space space space space straight p space equals space 1 half comma space space space straight q space equals space 1 minus 1 half space equals space 1 half$
P(at least 5 tails) = P(5) + P(6) + P(7)
$equals space straight C presuperscript 7 subscript 5 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses to the power of 5 plus space space straight C presuperscript 7 subscript 6 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 6 space plus space straight C presuperscript 7 subscript 7 space open parentheses 1 half close parentheses to the power of 7 space equals space open parentheses 1 half close parentheses to the power of 7 space open square brackets straight C presuperscript 7 subscript 5 space plus space straight C presuperscript 7 subscript 6 space plus space straight C presuperscript 7 subscript 7 close square brackets space equals space 1 over 128 open square brackets fraction numerator 7 space cross times 6 over denominator 1 cross times 2 end fraction plus 7 over 1 plus 1 close square brackets space equals space 1 over 128 left parenthesis 21 plus 7 plus 1 right parenthesis space equals space 29 over 128$

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Probability

A fair coin is tossed 7 times. Find the probability of obtaining at least 5 tails.

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