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, what is the probability that the coin will not be a $Rs.\ 5$ 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: 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 an $Rs.\ 5$ 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 an $Rs.\ 5$ coin is $\frac{17}{18}$

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