# Ex.15.1 Q11 Probability Solution - NCERT Maths Class 9

## Question

The blood groups of \(30\) students of **Class VIII** are recorded as follows:

\(A,\, B, \,O,\, O,\, AB,\, O,\, A,\, O,\,\\ B,\, A,\, O,\, B,\, A,\, O,\, O,\, A,\,\\ AB,\, O,\, A,\, A,\, O,\, O,\, AB,\,\\ B,\, A,\, O,\, B,\, A,\, B,\, O.\)

Use this table to determine the probability that a student of this class, selected at random, has blood group \(AB.\)

## Text Solution

**What is known?**

No of students and their blood group.

**What is unknown?**

Probability of students having blood group \(AB.\)

**Reasoning:**

The empirical probability \(P(E)\) of an event \(E\) happening, is given by:

\(\begin{align}{P}({E})=\frac{ \begin{pmatrix} \text { Number of trials in which }\\ \text{the event happened } \end{pmatrix} }{ \text { The total number of trials } }\end{align}\)

Use probability to derive the solution where

Probability (Of a selected student having a specific blood group)

\[\begin{align}\\&=\frac{ \begin{pmatrix}\text { Number of students having} \\ \text{ specific blood group} \end{pmatrix}}{\text { Total number of students }} \end{align}\]

**Steps:**

Total no of students \(= 30\)

No of students having blood group \(AB = 3\)

Probability \(P\) (Of a student having blood group \(AB\))

\(\begin{align}\\&=\frac{ \begin{pmatrix} \text { Number of students having} \\ \text{ blood group } AB \end{pmatrix} }{\text { Total number of students }} \\ &=\frac{3}{30} \\& =\frac{1}{10} \end{align}\)