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

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## 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}

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