A bag contains seven pennies, 10 nickels, and seven dimes. How many coins of each type should be added to increase the number of coins to 48
while keeping the probability of randomly selecting each type of coin the same?
In this question, we have a bag containing seven pennies, 10 nickels, and seven
dimes. This is a total of 24 coins. As such, the probabilities of randomly selecting a penny, nickel, or dime are seven
over 24, 10 over 24, and seven over 24, respectively, since the probability of an
event is equal to the number of favorable outcomes over the total possible number of
outcomes. Note that this holds when the probability of selecting each item is equally likely as
in this case.
We want these probabilities to remain the same whilst increasing the total number of
coins to 48. 24 multiplied by two is equal to 48. As such, we need to multiply the number of pennies, nickels, and dimes by two so that
the probabilities remain the same. Since seven multiplied by two is equal to 14 and 10 multiplied by two is equal to 20,
we will have a total of 14 pennies, 20 nickels, and 14 dimes in the bag.
We therefore need to add seven pennies, 10 nickels, and seven dimes so that the total
number of coins is 48 and the probability of selecting each type of coin at random
remains the same.