Question

quiz 6.4.1 - adding probabilities
this quiz will test your knowledge on when and how to add probabilities together.
value: 3
there are five nickels and seven dimes in your pocket. four of the nickels and six of the dimes are canadian. the others are us currency. you randomly select a coin from your pocket. what is the probability it is a nickel or it is canadian currency?
a. 11/12
b. 15/12
c. 5/36
d. 5/12

Explanation:

Step1: Calculate total number of coins

There are 5 nickels and 7 dimes, so the total number of coins is $5 + 7=12$.

Step2: Calculate number of nickels

The number of nickels $n(N)=5$.

Step3: Calculate number of Canadian - coins

The number of Canadian - coins is $4$ (Canadian nickels) $+ 6$ (Canadian dimes)$=10$.

Step4: Calculate number of Canadian nickels

The number of Canadian nickels $n(N\cap C)=4$.

Step5: Use the formula for $P(A\cup B)$

The formula for the probability of $A$ or $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, let $A$ be the event of selecting a nickel and $B$ be the event of selecting a Canadian - coin. $P(N)=\frac{n(N)}{n(T)}=\frac{5}{12}$, $P(C)=\frac{10}{12}$, and $P(N\cap C)=\frac{4}{12}$. Then $P(N\cup C)=\frac{5 + 10-4}{12}=\frac{11}{12}$.

Answer:

A. 11/12