# Ex.15.1 Q10 Probability Solution - NCERT Maths Class 10

## Question

A piggy bank contains hundred \(50\)\( \rm{p}\) coins, fifty \(\rm{Re}\) \(1\) coins, twenty \(\rm{Rs}\) \(2\) coins and ten \(\rm{Rs}\) \(5\) coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) will be a \(50\)\( \rm{p}\) coin?

(ii) will not be a \( \rm{Rs}\) \(5\) coin?

## Text Solution

**What is known?**

A piggy bank contains hundred \(50\) \(\rm{p}\) coins, fifty \( \rm{Re}\) \(1\) coins, twenty \(\rm{Rs}\) \(2\) coins and ten \(\rm{Rs}\) \(5\) coins. It is equally likely that one of the coins will fall out when the bank is turned upside down.

**What is unknown?**

The probability that the coin

(i) will be a \(50\)\( \rm{p}\) coin?

(ii) will not be a \( \rm{Rs}\) \(5\) coin?

**Reasoning:**

This question can be solved easily;

Find out the probability of getting \(50\)\( \rm{p}\) coin, \( \rm{Re}\) \(1\) coin and \( \rm{Rs}\) \(2\) coin by using the formula

Probability of an event

\[=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }\]

**Steps:**

We can use same approach as we used in question no 9.

Total no of coins

\(=100+50+20+10=180\)

No of \(50\) \(\rm{p}\) \(=100\)

No of \(1 \) \( \rm{Re}\) coins \(=50\)

No of \(2\) \( \rm{Rs}\) coins \(=20\)

No of \(5\) \( \rm{Rs}\) coins\(=10\)

(i) Probability of drawing \(50\)\( \rm{p}\) coin \(=\frac{100}{180}\)

(ii) Probability of getting a \( \rm{Rs}\) \(5\) coin \(=\frac{10}{180}=\frac{1}{18} \)

Probability of not getting a \( \rm{Rs}\) \(5\) coin \(=1-\frac{1}{18}=\frac{17}{18}\)