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

b. 3/4

Step-by-step 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)}=(6)/(12)`

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

`P(\text{even number)}=(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)}=(6)/(12)+(6)/(12)-(3)/(12) \\ =(9)/(12) \\ =(3)/(4) \end{gathered}`

The correct choice is B.