Question

Reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. If she chooses two of these coins at

random, what is the probability that the two coins together will be worth 50 cents?
A- 4/27
B- 5/18
C- 20/81
D- 1/6

Answer 1

B-5/18

Explanation:

There are two cases where Reyna can choose two coins that add up to 50 cents:

Case 1: She chooses two of the 5-cent coins. There are 5 choose 2 ways she can do this, or 10 ways.

Case 2: She chooses one 5-cent coin and one 25-cent coin. There are 5 x 4 = 20 ways she can choose one of the 5-cent coins and one of the 25-cent coins.

The total number of ways she can choose any two coins out of the nine coins is 9 choose 2, or 36 ways.

Therefore, the probability of choosing two coins that add up to 50 cents is (10 + 20)/36, which simplifies to 5/18.

So the answer is (B) 5/18.