A bag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies. If 2 coins are randomly chosen from the bag, one after the other, and not replaced, and if the total value of the chosen coins is 26 cents, what is the probability that a third coin randomly chosen from the bag will be a penny?
A)
1
3
B)
1
4
C)
3
13
D)
3
14
E)
3
4
A bag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies. If 2 coins are randomly chosen from the bag, one after the other, and not replaced, and if the total value of the chosen coins is 26 cents, what is the probability that a third coin randomly chosen from the bag will be a penny?
You're starting with 2 + 5 + 3 + 4 coins for a total of 14 coins.
There's only one way to make 26¢ with 2 coins, and that's a quarter and a penny.
So remaining in the bag are 1 + 5 + 3 + 3 coins for at total of 12 coins.
3 of those 12 coins are pennies, so the likelihood of randomly pulling a penny
is now 3 out of 12, this fraction reduces to 1 out of 4, so the answer is B. 1/4
