Question

quiz 6.4.1 - adding probabilities
this quiz will test your knowledge on when and how to add probabilities together.
value: 3
a box contains six red playing cards numbered one to six and also six black playing cards numbered one to six. what is the probability of picking a card that is black or has an even number?
a. 3/4
b. 1
c. 1/4
d. 1/2

Explanation:

Step1: Calculate total number of cards

There are 6 red and 6 black cards, so the total number of cards $n = 6+6=12$.

Step2: Calculate number of black cards

There are 6 black cards, so $n_{black}=6$.

Step3: Calculate number of even - numbered cards

The cards are numbered from 1 to 6. Among 12 cards, the even - numbered cards are 2, 4, 6 in red and 2, 4, 6 in black. So $n_{even}=6$.

Step4: Calculate number of black and even - numbered cards

The black and even - numbered cards are 2, 4, 6 in black, so $n_{black\ and\ even}=3$.

Step5: Use the addition rule for non - mutually exclusive events

The formula for $P(A\ or\ B)$ is $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$. Here, $A$ is the event of picking a black card and $B$ is the event of picking an even - numbered card. $P(A)=\frac{n_{black}}{n}=\frac{6}{12}$, $P(B)=\frac{n_{even}}{n}=\frac{6}{12}$, and $P(A\ and\ B)=\frac{n_{black\ and\ even}}{n}=\frac{3}{12}$. Then $P(A\ or\ B)=\frac{6 + 6-3}{12}=\frac{9}{12}=\frac{3}{4}$.

Answer:

A. 3/4