Question

We are drawing two cards without replacement from a standard​ 52-card deck. find the probability that we draw at least one red cardred card.

Answer 1

The probability of drawing only one red card in two draws without replacement is given by:
$P(1\ red)=\frac{26C1\times26C1}{52C2}=0.51$
The probability of drawing two red cards in two draws without replacement isgiven by:
$P(2\ red)=\frac{26C2\times26C0}{52C2}=0.245$
The events 'draw one red card' and 'draw two red cards' are mutually exclusive. Therefore the probability of drawing at least one red card is 0.51 + 0.245 = 0.755.