Question

One card is selected from a deck of playing cards. What is the probability that the card selected is either a club or a face card?

Answer 1

For this case we can define the following events:

C= the card selected is a club

F= the card selected is a face card

We want to find this probability:

`P(\text{CUF)}`

We can use the total rule of probability and we have:

`P(\text{CUF)}=P8C)+P(F)-P(C\cap F)`

And we can find the individual probabilities like this:

`P(C)=(13)/(52)`
`P(F)=(12)/(52)`

And the intersection is given by:

`P(C\cap F)=(3)/(52)`

Replacing we have:

`P(\text{CUF)}=(13)/(52)+(12)/(52)-(3)/(52)=(22)/(52)=(11)/(26)`

Then the answer is:

11/26