# Ex.15.1 Q4 Probability Solution - NCERT Maths Class 9

## Question

Three coins are tossed simultaneously \(200\) times with the following frequencies of different outcomes

If the three coins are simultaneously tossed again, compute the probability of \(2\) heads coming up.

## Text Solution

**What is known?**

Total number of tosses and frequencies of different outcomes.

**What is unknown?**

Probability of \(2\) heads coming up when three coins are tossed simultaneously.

**Reasoning:**

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

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

Use probability to derive the solution where

Probability of a particular outcome

\[\begin{align} & { = \frac{\begin{bmatrix}{\text{No of time of a particular }} \\ {\text{outcome occurs }}\end{bmatrix} }{{{\text{Total number of tosses}}}}} \end{align}\]

**Steps:**

Given total number of tosses \(= 200\)

No of \(2\) heads outcomes \(= 72\)

Probability [of head outcomes]

\[\begin{align} & { = \frac{ {\text{Number of times }} {\text{heads occur}} }{{{\text{Total number of tosses}}}}} \\ &=\frac{72}{200} \\ &=\frac{9}{25} \end{align}\]