Question

$A$ and $B$ toss 3 coins. The probability that both obtain same number of tails is $p$ and the probability that both obtain same number of heads is $q$, then the value of $p+q$ is

• A. $\frac{5}{16}$
• B. $\frac{10}{16}$
• C. $\frac{12}{16}$
• D. $\frac{7}{16}$

Answer 1

The correct option is B $\frac{10}{16}$

$A$ and $B$ can get $0$ tails or $1$ tail or $2$ tails or $3$ tails

The probability of getting $0$ tails or $3$ heads is $\frac{1}{8}\times \frac{1}{8}=\frac{1}{64}$.

The probability of getting $1$ tails or $2$ heads is $\frac{3}{8}\times \frac{3}{8}=\frac{9}{64}$.

The probability of getting $2$ tails or $1$ head is $\frac{3}{8}\times \frac{3}{8}=\frac{9}{64}$.

The probability of getting $3$ tails or $0$ heads is $\frac{1}{8}\times \frac{1}{8}=\frac{1}{64}$.

The value of $p$ is equal to value of $q$.

$\Rightarrow p=q=\frac{1}{64}+\frac{1}{64}+\frac{9}{64}+\frac{9}{64}=\frac{20}{64}=\frac{5}{16}$

Therefore the value of $p+q$ is $\frac{10}{16}$

Therefore option $B$ is correct.