Question

A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

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

Given:

A die is rolled and coin is tossed.

To find:

The probability that the die shows an odd number and the coin shows a head

All the possible outcomes = $(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)$

Total number of possible outcomes = $12$

Favourable outcomes of the die showing an odd number and the coin showing a head = $(1,H),(3,H),(5,H)$

Number of favourable outcomes = $3$

Hence, the probability that the die shows an odd number and the coin shows a head

$P\left(\text{getting an odd number on die and head on coin}\right)=\frac{\text{No. of favourable ways}}{\text{Total number of ways}}=\frac{3}{12}=\frac{1}{4}$