Cards: prob both cards, drawn w/o replacement, are black

[kblunt82]

2 cards are drawn from an ordinary deck without replacement. What is the probability that at least one card is black?

I am leaning towards subtracting the probability that they are both black from the probability that one is black on the first draw??? I am confusing myself and need help please!!!!

 

[soroban]

Hello, kblunt82!

Two cards are drawn from an ordinary deck without replacement.
What is the probability that at least one card is black?

The opposite of "at least one black" is "NO black" . . . "both red".

\(\displaystyle \text{The probability of both red is: }\(\text{two red}) \:=\:\frac{26}{52}\cdot\frac{25}{51} \:=\:\frac{25}{102}\)

\(\displaystyle \text{Therefore: }\(\text{at least one black}) \;=\;1 - \frac{25}{102} \;=\;\boxed{\frac{77}{102}}\)