Question

A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ .The probability of hitting the target $5^{th}$ time at the $10^{th}$ throw is :

• A. $\frac{5}{2^{10}}$
• B. $\frac{63}{2^{9}}$
• C. $\frac{^{10}C_5}{2^{10}}$
• D. None

Answer 1

The Correct Option is B

The probability of hitting the target $5^{\text {th }}$ time at the $10^{\text {th }}$ throw $=$ (the probability of hitting the target $4$ times in the first $9$ throws) $\times$ (the probability of hitting the target at the $10^{\text {th }}$ throw)
$={ }^{9} C_{4}\left(\frac{1}{2}\right)^{9} \times \frac{1}{2} $
$={ }^{9} C_{4}\left(\frac{1}{2}\right)^{10} $
$=\frac{9.8 .7 .6}{(1.2 .3 .4) 2^{10}}=\frac{63}{2^{9}}$