# 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]

Video Solution
Probability
Ex 15.1 | Question 24

## 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:

Probability of an event

$=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }$

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} & = \begin{bmatrix} \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),\left( 2,5 \right), \\ \left( 3,5 \right),\left( 4,5 \right),\left( 6,5 \right) \end{bmatrix} \\&=11\end{align}

probability that $$5$$ will come up either time

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ & =\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{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ & =\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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