Question

# take two cards from a deck without replacement. what is the probability of getting a red queen and then another red card

Probability and combinatorics
take two cards from a deck without replacement. what is the probability of getting a red queen and then another red card

2021-06-20

There are 2 red queens (hearts and diamonds) in a standard deck of cardsso the probability of drawing a red queen is:
$$\displaystyle\frac{{2}}{{52}}=\frac{{1}}{{26}}$$
Since there is no replacement, there remains a total of $$13 + 12 = 25$$ red cards out of the remaining 51 cards so the probability that the next crad drawn is a red card is:
$$\displaystyle\frac{{25}}{{51}}$$
Hence, the probability of getting a red queen and then another red card is the product of the probabilities:
$$\displaystyle\frac{{1}}{{26}}\cdot\frac{{25}}{{51}}=\frac{{25}}{{1326}}$$