# Ex.15.1 Q24 Probability Solution - NCERT Maths Class 10

## Question

A die is thrown twice. What is the probability that

(i) \(5\) will not come up either time?

(ii) \(5\) will come up at least once?

[**Hint:** Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

## Text Solution

**What is known?**

A die is thrown twice.

**What is unknown?**

The probability that (i) \(5\) will not come up either time? (ii) \(5\) will come up at least once?

**Reasoning:**

\[\text{Probability of an event}=\frac{\text{ Number of possible outcomes }}{\text{Total no of favourable outcomes}}\]

Probability of not happening an event is equal to \(1\) minus probability of happening an event.

**Steps:**

(i) No of possible outcomes when \(5\) will come up either time

\[\begin{align}&=\left( 5,1 \right),\left( 5,2 \right),\left( 5,3 \right),\left( 5,4 \right),\left( 5,5 \right),\left( 5,6 \right),\left( 1,5 \right),\\&\quad\quad\left( 2,5 \right),\left( 3,5 \right),\left( 4,5 \right),\left( 6,5 \right)\\&=11\end{align}\]

probability that \(5\) will come up either time

\[\begin{align} & =\frac{\text{ Number of possible outcomes }}{\text{ Total no of favorable outcomes}} \\ {} & =\frac{11}{36} \\\end{align}\]

probability that \(5\) will not come up either time

\[\begin{align} & =1-\frac{11}{36} \\{} & =\frac{25}{36} \\\end{align}\]

(ii) No of possible outcomes when \(5\) will come up at-least once = \(11\)

probability that \(5\) will come up at-least once

\[\begin{align}&=\frac{\text{Number of possible outcomes}}{\text{Total no of favorable outcomes}} \\ & =\frac{11}{36} \\\end{align}\]

probability that \(5\) will not come up either time is \(\begin{align}\frac{25}{36}\end{align}\) and probability that \(5\) will come up at least once is \(\begin{align}\frac{11}{36}\end{align}\)