Question

If $A$ and $B$ are two equally strong table tennis players, the probability that $A$ beats $B$ in exactly three games out of $4$ games is

• A. $\frac{1}{6}$
• B. $\frac{1}{5}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{1}{4}$

$A$ and $B$ are two equally strong table tennis players, probability of success that $A$ beats $B$ $=\frac{1}{2}$
The probability that $A$ beats $B$ in exactly three games out of $4$ games
${=}^n{C}_k{p}^k{(1-p)}^{n-k}$

${=}^4{C}_3{(\frac{1}{2})}^3{(1-\frac{1}{2})}^{4-3}$
$=4\times \frac{1}{16}$
$=\frac{1}{4}$