A piggy bank contains hundred 50 p coins, fifty ₹ 1 coins, twenty ₹ 2 coins and ten ₹ 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 will not be a ₹ 5 coin?
Given:
A piggy bank contains hundred $50\ p$ coins, fifty $Rs.\ 1$ coins, twenty $Rs.\ 2$ coins and ten $Rs.\ 5$ coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down.
To do:
We have to find the probability that the coin will not be a $Rs.\ 5$ coin.
Solution:
Total number of coins in the piggy bank $=100+50+20+10=180$
Let $E$ be the event of getting a $Rs.\ 5$ coin.
Number of possible outcomes $=180$
Number of outcomes favorable to event $E=10$
$\therefore P( E) = \frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
$= \frac{10}{180}$
$= \frac{1}{18}$
$\therefore P( not\ getting\ a\ Rs.\ 5\ coin )=P(\overline E)$
$= 1 - P( E)$
$= 1 - \frac{1}{18}$
$= \frac{17}{18}$
Therefore, the probability of not getting a $Rs.\ 5$ coin is $\frac{17}{18}$.
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