Question

A single card is drawn from a standard​ 52-card deck. Let D be the event that the card drawn is a black card​, and let F be the event that the card drawn is a 10 card. Find the indicated probability.

P(DUF')

The probability P(DUF') is

Answer 1

`(25)/(26)`

Explanation:

Let

• D be the event that the card drawn is a black card​
• F be the event that the card drawn is a 10 card
• F' be the event that the card drawn is not a 10 card

The probability

`Pr(D\cup F')=Pr(D)+Pr(F')-Pr(D\cap F')\\`

Note that

`Pr(D)=(26)/(52)=(1)/(2)\\ \\Pr(F)=(4)/(52)=(1)/(13)\\ \\Pr(F')=1-(1)/(13)=(12)/(13)\\ \\Pr(D\cap F')=(24)/(52)=(6)/(13)`

So,

`Pr(D\cup F')=(1)/(2)+(12)/(13)-(6)/(13)=(25)/(26)`