Question

A coin is tossed 7 times. What is the probability that tail appears an odd number of times?

Solution

Here n = 7
p = P(tail in one toss) = $1 half comma$ $therefore space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 half space equals space 1 half$
P(tails appears on odd number of times) = P(1) + P(3) + P(5) + P(7)
$equals space straight C presuperscript 7 subscript 1 space open parentheses 1 half close parentheses to the power of 6 space open parentheses 1 half close parentheses space plus space straight C presuperscript 7 subscript 3 space open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses cubed space plus space straight C presuperscript 7 subscript 5 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses to the power of 5 space plus space straight C presuperscript 7 subscript 7 space open parentheses 1 half close parentheses to the power of 7 space equals space open parentheses 1 half close parentheses to the power of 7 space open square brackets straight C presuperscript 7 subscript 1 space plus space straight C presuperscript 7 subscript 3 space plus space straight C presuperscript 7 subscript 5 space plus space straight C presuperscript 7 subscript 7 close square brackets space equals space 1 over 128 space open square brackets 7 over 1 cross times fraction numerator 7 cross times 6 cross times 5 over denominator 1 cross times 2 cross times 3 end fraction plus fraction numerator 7 cross times 6 over denominator 1 cross times 2 end fraction plus 1 close square brackets equals space 1 over 128 left square bracket 7 plus 35 plus 21 plus 1 right square bracket space equals 64 over 128 equals 1 half$

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Probability

A coin is tossed 7 times. What is the probability that tail appears an odd number of times?

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