Question

A coin and six faced die, both unbiased are thrown simultaneously. The probability of getting a tail on the coin and an even number on the die is:

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

Answer 1

The correct option is C

$\frac{1}{4}$

Explanation of the correct option:

Finding the required probability:

Let $E$ be the event of getting a tail on the throw of coin. On throw of a coin, we can get either a head or a tail.

$\Rightarrow P\left(E\right)=\frac{1}{2}$

Let $F$ be the event of getting an even number on the throw of die. On throw of a die, we can obtain any number between $1\mathrm{to}6$ of which three numbers are even ($2,4,6$).

$\begin{array}{rcl}& \Rightarrow & P\left(F\right)=\frac{3}{6}\\ & =& \frac{1}{2}\end{array}$

We have to find the probability of getting a tail on the coin and an even number on the die.

Therefore, the required probability will be $=P\left(E\cap F\right)$

$\begin{array}{rcl}P\left(E\cap F\right)& =& \frac{1}{2}\times \frac{1}{2}\\ & =& \frac{1}{4}\end{array}$

Hence, the correct answer is option C.