# Ex.15.1 Q23 Probability Solution - NCERT Maths Class 10

## Question

A game consists of tossing a one rupee coin \(3\) times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

## Text Solution

**What is known?**

A game consists of tossing a one rupee coin \(3\) times

\(= \begin{Bmatrix} \text{HHH,TTT,HTH,HHT,} \\ \text{THH,THT,TTH,HTT} \end{Bmatrix} =8\)

Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise.

**What is unknown?**

The probability that Hanif will lose the game.

**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:**

Probability that Hanif will win the game

\[\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ & =\frac{2}{8}\\&=\frac{1}{4} \end{align}\]

Probability that Hanif will lose the game

\[\begin{align} & =1-\frac{1}{4} \\ & \,=\frac{3}{4} \\\end{align}\]

The probability that Hanif will lose the game is \(\frac{3}{4} \)