Question

A piggy bank contains 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 will be a 50 paise win will be of value more than Rs. 1 will be of value less than Rs. 5 will be a Rs. 1 or Rs. 2 coin.

Answer 1

Total number of coins = `(100+50+20+10) = 180`.
So, the number of all possible outcomes a 50-p coin.
Then, the number of favourable outcomes = 100.
`:. ` P(getting a 50-p coin) = `P(E_(1)) = 100/180 = 5/9`.
(ii) Let `E_(2)` be the evnet of getting coin of value more than Rs. 1.
Then, it can be Rs. 2 or Rs. 5 coin.
Number of all such coins = ` 20 + 10 = 30`.
` :. ` P(getting a coin of value more than Rs. 1)
` = P(E_(2)) = 30/180 = 1/6`.
(iii) Let ` E_(3)` be the event of getting a coin of value less than Rs.5 .
Then, it can be 50-p or Rs. 1 or Rs. 2 coin.
Number of favourable outcomes
= number of all coins of 50-p , Rs. 1 and Rs. 2
` = (100+50+20) = 170`.
` :. ` P(getting a coin of value less than Rs. 5)
` = P(E_(3)) = (170)/(180) = 17/18. `
(iv) Let ` E_(4)` be the event of getting a Rs. 1 or Rs. 2 coin.
Number of all such coins = 50+20 = 70.
Number of favourable outcomes = 70.