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. $\frac{{}^{10}{C}_4}{2^{10}}$

Answer 1

The correct option is B $\frac{63}{2^9}$

The probability of hitting the target $5^{th}$ time at the ${10}^{th}$ throw = (the probability of hitting the target 4 times in the first 9 throws) $\times$ (the probability of hitting the target at the 10^th throw)
${=}^9{C}_4{\left(\frac{1}{2}\right)}^9\times \frac{1}{2}{=}^9{C}_4{\left(\frac{1}{2}\right)}^{10}=\frac{\mathrm{9.8.7.6}}{\left(\mathrm{1.2.3.4}\right)2^{10}}=\frac{63}{2^9}$