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

Answer:

$\dfrac{25}{26}$

Step-by-step 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

$Pr(D)=\dfrac{26}{52}=\dfrac{1}{2}\\ \\Pr(F)=\dfrac{4}{52}=\dfrac{1}{13}\\ \\Pr(F')=1-\dfrac{1}{13}=\dfrac{12}{13}\\ \\Pr(D\cap F')=\dfrac{24}{52}=\dfrac{6}{13}$

So,

$Pr(D\cup F')=\dfrac{1}{2}+\dfrac{12}{13}-\dfrac{6}{13}=\dfrac{25}{26}$