Question

A coin purse contains 4 quarters and 6 dimes. Two coins are drawn at random without replacement. Find the probability that at least one of the two coins is a quarter.

Answer 1

Answer:

P(at least one of the two coins is a quarter) = 2/3

Step-by-step explanation:

Number of quarters = 4

Number of dimes = 6

Total number of coins = 10

P(At least one of the two coins is a quarter) = P(one is a quarter) + P(the two coins are quarters)

P(one of the coins is a quarter) = (4/10)(6/9) + (6/10)(4/9)

P(one of the coins is a quarter) = 24/90 + 24/90

P(one of the coins is a quarter) = 48/90

P(one of the coins is a quarter) = 8/15

P(the two coins are quarters) = (4/10)(3/9)

P(the two coins are quarters) = 12/90

P(the two coins are quarters) = 2/15

P(At least one of the two coins is a quarter) = 8/15 + 2/15

P(At least one of the two coins is a quarter) = 10/15

P(at least one of the two coins is a quarter) = 2/3