Question

Four unbiased coins, a quarter (25 cent coin), a dime (10 cents coin) and two different nickles (5 cent coins, one minted before year 2000 and other after Year 2000) are tossed simultaneously. If a head shows up on any coin, you are paid the amount on the coin but for tail, you are paid no money for that coin. Find the probability that upon a single simultaneous toss of all four coins, you are paid a total of 35 cents or more

Answer 1

Solution :

We can be paid 35 cents or more by following events :

A : Head shows on quarter coin, head shows on a 10 cent coin

B : Head shows on quarter coin, head shows on 10 cent coin and head shows on any one coin of two 5 cent coins.

C : Head shows on quarter coin, head shows on 10 cent coin and head shows on both of the 5 cent coins

D : Head shows on quarter coin and head shows on both of the 5 cent coins.

Probability of obtaining a head on any coin = 1/2

Hence, P(A) = (1/2) × (1/2) = 1/4

P(B) = [(1/2) × (1/2) × (1/2)] × 2= 1/4

P(C) = (1/2) × (1/2) × (1/2) × (1/2) = 1/16

P(D) = (1/2) × (1/2) × (1/2) = 1/8

Hence, probability that upon a single simultaneous toss of all four coins, you are paid a total of 35 cents or more is,

P(35 or more) = P(A) + P(B) + P(C) + P(D)

P(35 or more) = (1/4) + (1/4) + (1/16) + (1/8)

P(35 or more) = (4 + 4 + 1 + 2)/16

P(35 or more) = 11/16

P(35 or more) = 0.6875

Hence, the probability that upon a single simultaneous toss of all four coins, you are paid a total of 35 cents or more is 0.6875.