Question

An international bank contains 2 quarters, 3 dimes, 4 nickels, and 5 pennies. One coin is removed at random. What is the probability that the coin is a quarter or a nickel?
A) \[\dfrac{1}{7}\]
B) \[\dfrac{4}{3}\]
C) \[\dfrac{2}{{14}}\]
D) \[\dfrac{3}{7}\]

Answer 1

Hint: Here we will first find the total number of coins and then we will apply the formula for probability. Probability is the ratio of the number of favorable outcomes to the total number of outcomes.
\[{\text{Probability}} = \dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total outcomes}}}}\]

Complete step by step answer:
It is given that international bank contains 2 quarters, 3 dimes, 4 nickels, and 5 pennies
Therefore, we will first calculate the total number of coins.
\[{\text{Total coins}} = 2 + 3 + 4 + 5\]
Solving it further we get:-
\[\Rightarrow {\text{Total coins}} = 14\]
Hence we get the total number of outcomes to be 14.
Now since we have to find the probability of a coin is a quarter or a nickel.
Hence we need to find the number of coins that are quarter or nickel.
Hence we get:-
\[\Rightarrow {\text{Number of coins quarter or nickel}} = 2 + 4{\text{ }}\]
Solving it further we get:-
\[\Rightarrow {\text{Number of coins quarter or nickel}} = 6{\text{ }}\]
Hence we get the number of favorable outcomes to be 6
Now applying the formula for probability
\[{\text{Probability}} = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total outcomes}}}}\]
Putting in the values we get:-
\[\Rightarrow {\text{Probability}} = \dfrac{{\text{6}}}{{{\text{14}}}}\]
Simplifying it further we get:-
\[\Rightarrow {\text{Probability}} = \dfrac{3}{7}\]

Hence, option (D) is the correct option.

Note:
Students should note that the probability of any event is always less than or equal to 1.
Also, we have to add the number of events in case of “either-or”.