Question

A coin is tossed 10 times, probability that on the ${10}^{th}$ throw to observed $5^{th}$ head is

• A. ${}^9{\text{C}}_5\frac{1}{2^5}$
• B. $\frac{{}^9{\text{C}}_4}{2^{10}}$
• C. $\frac{{}^9{\text{C}}_5}{2^{10}}$
• D. None of these

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{{}^9{\text{C}}_4}{2^{10}}$
C $\frac{{}^9{\text{C}}_5}{2^{10}}$

Since $5^{th}$ head is needed on the tenth throw, 4 heads have already been appeared in the previous 9 throws.
Thus, the required probability equals ${}^9{C}_4\left(\frac{1}{2}{)}^5\right(\frac{1}{2}{)}^4\left(\frac{1}{2}\right){=}^9{C}_4(\frac{1}{2}{)}^{10}$
${}^9{C}_4{=}^9{C}_5$ and so option c is also correct.