# Question 1 Exercise 6.4

Solutions of Question 1 of Exercise 6.4 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

## Question 1(a)

Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the probability of rolling a $5$ ?

### Solution

Rolling a $5$ Let \begin{align}A&=\{5\}\\ P(A)&=\dfrac{n(A)}{n(S)}\\ &=\dfrac{1}{6} \end{align}

## Question 1(b)

Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the probability of rolling a number less than $1$ ?

### Solution

Rolling a number less than $1$ Let \begin{align}B&=\{\}\\ &=\phi \text{then}\\ P(B)&=\dfrac{n(B)}{n(S)}\\ &=\dfrac{0}{6}\\ &=0\end{align}

## Question 1(c)

Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the probability of rolling a number greater than $0$ ?

### Solution

Rolling a number greater than $0$ Let \begin{align}C&=\{1,2,3,4,5,6\},\text{then}\\ P(C)&=\dfrac{n(C)}{n(S)}\\ &=\dfrac{6}{6}\\ &=1\end{align}

## Question 1(d)

Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the probability of rolling a multiple of $3$ ?

### Solution

Rolling a multiple of $3$ Let \begin{align}D&=\{3,6\}\text{then}\\ P(D)&=\dfrac{n(D)}{n(S)}\\ &=\dfrac{2}{6}\\ &=\dfrac{1}{3}\end{align}

## Question 1(e)

Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the probability of rolling a number greater or equal to $4$ ?

### Solution

Rolling a number greater than or equal to $4$ Let \begin{align} E &=\{4,5,6\}\text{then}\\ P(E)&=\dfrac{n(E)}{n(S)}\\ &=\dfrac{3}{6}\\ &=\dfrac{1}{2}\end{align}

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