A piggy bank contains hundred 50 paise coins, fifity ₹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, find the probability that the coin which fell
(i)will be a 50 paise coin
(ii)will be of value more than ₹1
(iii)will be of value less than ₹5
(iv)will be a ₹1 or ₹2 coin
Answers
SOLUTION :
Given : Number of 50 paise coins in a piggy bank = 100
Number of ₹1 coins in a piggy bank = 50
Number of ₹2 coins in a piggy bank = 20
Number of ₹5 coins in a piggy bank = 10
Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180
Total number of possible outcomes = 180
(i)Let E1 = Event of getting the coin which fell will be a 50 paise coin
Number of 50 paise coins in a piggy bank = 100
No. of favourable outcomes = 100
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 100/180 = 10/18 = 5/9
Hence, the required probability of getting the coin which fell will be a 50 paise coin,P(E1) = 5/9.
(ii)Let E2 = Event of getting the coin which fell will be of value more than ₹1 i.e ₹2 & ₹5 coins
Number of coin which fell will be of value more than ₹1 = 20 + 10 = 30
No. of favourable outcomes = 30
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = 30/180 = 3/18 = 1/6
Hence, the required probability of getting the coin which fell will be of value more than ₹1 ,P(E2) = ⅙ .
(iii)Let E3 = Event of getting the coin which fell will be of value less than ₹5 i.e 50 paise ₹1 & ₹2 coins
Number of coin which fell will be of value more than ₹1 = 100 + 50 + 20 = 170
No. of favourable outcomes = 170
Probability (E3) = Number of favourable outcomes / Total number of outcomes
P(E3) = 170/180 = 17/18
Hence, the required probability of getting the coin which fell will be of value less than ₹5 ,P(E3) = 17/18.
(iii)Let E4 = Event of getting the coin which fell will be of ₹1 & ₹2 coins
Number of coin which fell will be of ₹1 & ₹2 coins= 50 + 20 = 70
No. of favourable outcomes = 70
Probability (E4) = Number of favourable outcomes / Total number of outcomes
P(E4) = 70/180 = 7/18
Hence, the required probability of getting the coin which fell will be of ₹1 & ₹2 coins ,P(E4) = 7/18.
HOPE THIS ANSWER WILL HELP YOU…
(i) 100/180=5/9
(II) 30/180=1/6
(iii) 170/180=17/18
(iv) 70/180=7/18
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