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# A piggy bank contains a hundred 50 paise 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, find the probability that the coin which fell(i) will be a 50 paise coin (ii) will be of value more than Rs.1(iii) will be of value less than Rs.5 (iv) will be Rs.1 or Rs.2 coin

Last updated date: 24th Mar 2023
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Hint: Use the ratio of probability that is number of favourable outcomes and the total number of outcomes.
We have been given hundred 50 paise coins, fifty Rs.1 coins, twenty Rs.2 coins and ten Rs.5 coins
The total number of coins that we have in the piggy bank is
$= 100 + 50 + 20 + 10 \\ = 180 \\$
Now for (i)
We have to find the probability that the coin which fell will be a 50 paise coin
So the event of getting a 50 paise coin is the favourable event
This implies that Number of Favourable Outcomes $= 100$
Now, as we know that
${\text{Probability}} = \dfrac{{{\text{Number of Favourable Outcomes}}}}{{{\text{Total number of Outcomes}}}}$
$\Rightarrow {\text{Probability}} = \dfrac{{100}}{{180}} = \dfrac{5}{9}$
Therefore, the probability that the coin which fell will be a 50 paise coin is $\dfrac{5}{9}$.

For (ii)
We have to find the probability that the coin which fell will be of value more than Rs.1
So, the event of getting a Rs.2 or Rs.5 coin is the favourable event
This implies that Number of Favourable Outcomes $= 20 + 10 = 30$
Now, as we know that
${\text{Probability}} = \dfrac{{{\text{Number of Favourable Outcomes}}}}{{{\text{Total number of Outcomes}}}}$
$\Rightarrow {\text{Probability}} = \dfrac{{30}}{{180}} = \dfrac{1}{6}$
Therefore, the probability that the coin which fell will be of value more than Rs.1 is $\dfrac{1}{6}$.

For (iii)
We have to find the probability that the coin which fell will be of value less than Rs.5
So, the event of getting a 50 paise coin or Rs.1 or Rs.2 coin is the favourable event
This implies that Number of Favourable Outcomes $= 100 + 50 + 20 = 170$
Now, as we know that
${\text{Probability}} = \dfrac{{{\text{Number of Favourable Outcomes}}}}{{{\text{Total number of Outcomes}}}}$
$\Rightarrow {\text{Probability}} = \dfrac{{170}}{{180}} = \dfrac{{17}}{{18}}$
Therefore, the probability that the coin which fell ) will be of value less than Rs.5 is $\dfrac{{17}}{{18}}$.

For (iv)
We have to find the probability that the coin which fell will be a Rs.1 or Rs.2 coin.
So, the event of getting a Rs.1 or Rs.2 coin is the favourable event
This implies that Number of Favourable Outcomes $= 50 + 20 = 70$
Now, as we know that
${\text{Probability}} = \dfrac{{{\text{Number of Favourable Outcomes}}}}{{{\text{Total number of Outcomes}}}}$
$\Rightarrow {\text{Probability}} = \dfrac{{70}}{{180}} = \dfrac{7}{{18}}$
Therefore, the probability that the coin which fell ) will be of value less than Rs.5 is $\dfrac{7}{{18}}$.

Note: In this question we first find the total number of possible outcomes and then find the number of favourable outcomes for each case. Then using the formula of probability we get our answer.