Question

A coin and a die is tossed simultaneously. Find the probability of the event that 'tail' and a prime number turns up?

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

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

Let $S$ be the sample space.

$\therefore S=\left\{\right(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6\left)\right\}$

$n\left(S\right)=12$

Let $A$ be the event of getting tail and a prime number.

$\therefore A=\left\{\right(T,2),(T,3),(T,5\left)\right\}$

$⟹$ $n\left(A\right)=3$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{3}{12}=\frac{1}{4}$

Hence, option B is correct.