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?

Question

asked Oct 22, 2023 42.2k views

1 Answer

PankajSharma · Answer 1 · 2023-10-26T17:55:36+0000

Solution

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:

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