Question

A box contains six red and 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. 1 b. ¾c. ½d. ¼

Answer 1

Answer:

b. 3/4

Explanation:

• Number of black cards = 6

,

• Number of red cards = 6

,

• The total number of cards = 6+6 =12

,

• The number of cards with even numbers (2,4, and 6) = 6

First, calculate the probability of picking a card that is black.

$P(\text{black)}=\frac{6}{12}$

Next, calculate the probability of picking a card that has an even number.

$P(\text{even number)}=\frac{6}{12}$

Now, by probability theory:

$P(A\text{ or B)=P(A)+P(B)-P(}A\cap B)$

However, there are 3 black cards that have even numbers, therefore:

$\begin{gathered} P(\text{black or even)}=\frac{6}{12}+\frac{6}{12}-\frac{3}{12} \\ =\frac{9}{12} \\ =\frac{3}{4} \end{gathered}$

The correct choice is B.