Ex.15.1 Q10 Probability Solution - NCERT Maths Class 10

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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 \(\begin{align}=\frac{\text{Number of possible outcomes}}{\text{Total no of favourable outcomes}}\end{align}\)

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 \(\begin{align}=\frac{100}{180}\end{align}\)

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

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