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  • A fair coin is tossed tIII a head appears for the first time. The probability that the number of required tosses is odd, is  Option: 1 <i

A fair coin is tossed tIII a head appears for the first time. The probability that the number of required tosses is odd, is
 

Option: 1

\frac{1}{3}


Option: 2

\frac{1}{2}


Option: 3

\frac{2}{3}


Option: 4

\frac{3}{4}


Answers (1)

best_answer
Number of tosses Outcome Requried Probablility
1 H \frac{1}{2}
3 TTH \left ( \frac{1}{2} \right )^{3}
5 TTTTH \left ( \frac{1}{2} \right )^{5}
: : :

Requried Probability

                          
\mathrm{ =\frac{1}{2}+\left(\frac{1}{2}\right)^3+\left(\frac{1}{2}\right)^5+\ldots }

\mathrm{ =\frac{\frac{1}{2}}{1-\left(\frac{1}{2}\right)^2}=\frac{\frac{1}{2}}{\frac{3}{4}} }

=\frac{2}{3}
 

Posted by

Devendra Khairwa

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