A piggy bank contains hundred 50-p coins, seventy RS. 1 coin, fifty RS. 2 coins thirty 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 (i) will be a RS. 1 coin? (ii) will not be a RS. 5 coin (iii) will be 50-p or a RS. 2 coin?

Question

Philoid · Accepted Answer

Total numbers of elementary events are: 100 + 70 + 50 + 30 = 250 being number of coins of each denomination added to find total number of coins

(i) let E be the event of getting Rs. 1 coin

Then, numbers of favourable events = 70

∴ P (Rs 1 coin) = P (E) = 70/250 = 7/25

(ii) Let E be the event of not getting Rs 5 coin

Let A be the event of getting Rs 5 coin

Then, the numbers of favourable events = 30

P (Rs 5 coin) = P (A) = 30/250 = 3/25

∴ P (not Rs 5 coin) = P (E) = 1 – P (A) = 1 – 3/25 = 22/25

(iii) Let E be the event of getting 50-p or Rs2 coin

Let A be the event of getting 50-p coin

Then numbers of favourable outcomes = 100

P (50-p coin) = P (A) = 100/250 = 1/25

Let B be the event of getting Rs2 coin

Then numbers of favourable outcomes = 50

P (Rs2 coin) = P (B) = 50/250 = 5/25

∴ P (50-p coin or Rs2 coin) = P (E) = P (A) + P (B) = 1/25 + 5/25= 6/25