Question

A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is.

• A. $\frac{1}{8}$
• B. $\frac{1}{12}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is B

$\frac{1}{12}$

Explanation for the correct answer: -

Step 1: - Find the probability of each event

Let, event A: a coin shows the head after tossing.

event B: a dice shows 6 after rolling.

Probability of event A: -

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

Probability of event B:-

$P\left(B\right)=\frac{1}{6}$

Step 2: - Find the required probability

Event A and event B are independent events.

So, the probability that the coin shows the head and the dice shows 6 is

$$\begin{gathered} P=P\left(A\right)\times P\left(B\right) \\ \Rightarrow P=\frac{1}{2}\times \frac{1}{6} \\ \Rightarrow P=\frac{1}{12} \end{gathered}$$

Hence, option (B) is the correct answer.