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Probability

Question
CBSEENMA12033887
Wired Faculty App

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

Solution

Here n = 5
therefore space space straight p space equals space straight P left parenthesis head space in space one space toss right parenthesis space equals space 1 half therefore space space straight q space equals space 1 space minus space straight p space equals space 1 minus 1 half space equals space 1 half
                    straight P left parenthesis head space appearing space odd space number space of space times right parenthesis               equals space straight P left parenthesis straight r space equals space 1 comma space space 3 space space or space space 5 right parenthesis space equals space straight P left parenthesis 1 right parenthesis space plus space straight P left parenthesis 3 right parenthesis space space plus straight P left parenthesis 5 right parenthesis space equals space straight C presuperscript 5 subscript 1 space open parentheses 1 half close parentheses to the power of 5 minus 1 end exponent space open parentheses 1 half close parentheses to the power of 1 space plus space straight C presuperscript 5 subscript 3 space open parentheses 1 half close parentheses to the power of 5 minus 3 end exponent 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 0 space open parentheses 1 half close parentheses to the power of 5 space equals 5 over 1 cross times 1 over 16 cross times 1 half plus fraction numerator 5 cross times 4 cross times 3 over denominator 1 cross times 2 cross times 3 end fraction cross times 1 fourth cross times 1 over 8 plus 1 cross times 1 cross times 1 over 32 equals space 1 over 32 left parenthesis 5 plus 10 plus 1 right parenthesis space equals 16 over 32 space equals 1 half

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