# Ex.5.2 Q4 Data Handling Solutions - NCERT Maths Class 8

## Question

Numbers \(1\) to \(10\) are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it.

What is the probability of:

(i) getting a number \(6?\)

(ii) getting a number less than \(6?\)

(iii) getting a number greater than \(6?\)

(iv) getting a number less than \(6?\)

(v) getting a \(1-\)digit number?

## Text Solution

**What is known?**

Numbers \(1\) to \(10\) are written on ten separate slips (one number on one slip), kept in a box and mixed well

**What is unknown?**

(i) Probability of getting a number \(6\)

(ii) Probability of getting a number less than \(6 \)

(iii) Probability of getting a number greater than \(6\)

(iv) Probability of getting a number less than \(6\)

(v) Probability of getting a \(1-\)digit number

**Reasoning:**

Probability\(\begin{align} = \frac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\end{align}\)

**Steps:**

(i) Outcome of getting a number \(6\) from ten separate slips is \(1\). Therefore, probability of getting a number \(\begin{align}6 = \frac{1}{{10}}\end{align}\)

(ii) Numbers less than \(6\) are \(1, 2, 3, 4\) and \(5\). So, there are \(5\) outcomes. Therefore, probability of getting a number less than

\[\begin{align} 6 = \frac{5}{{10}} = \frac{1}{2} \end{align}\]

(iii) Number greater than 6 are \(7, 8, 9, 10.\) So there are \(4\) possible outcomes. Therefore, probability of getting a number greater than

\[\begin{align} 6 = \frac{4}{{10}} = \frac{2}{5} \end{align}\]

(iv) One-digit numbers are

\(1, 2, 3, 4, 5, 6, 7, 8, 9\) out of ten.

Therefore, probability of getting a \(1\)-digit number

\[\begin{align} = \frac{9}{{10}} \end{align}\]