A coin is tossed 5 times. What is the probability that head appears an odd number of times?

Solution

Here n = 5
p = P(head) = $1 half comma space space space straight q space equals space 1 minus 1 half space equals space 1 half$
P(head appears an odd number of times) = P(1) + P(3) + P(5)
$equals space straight C presuperscript 5 subscript 1 space open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses space plus space straight C presuperscript 5 subscript 3 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses cubed space plus space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 space equals space open parentheses 1 half close parentheses to the power of 5 space open square brackets straight C presuperscript 5 subscript 1 space plus space straight C presuperscript 5 subscript 3 space plus space straight C presuperscript 5 subscript 3 close square brackets space equals space 1 over 32 open square brackets 5 over 1 cross times fraction numerator 5 cross times 4 over denominator 1 cross times 2 end fraction plus 1 close square brackets space equals 1 over 32 left square bracket 5 plus 10 plus 1 right square bracket space equals space 16 over 32 equals space 1 half$

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Probability

A coin is tossed 5 times. What is the probability that head appears an odd number of times?

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