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
ANSWERED
asked 2021-06-19
take two cards from a deck without replacement. what is the probability of getting a red queen and then another red card

Expert Answers (1)

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:
\(\displaystyle\frac{{1}}{{26}}\cdot\frac{{25}}{{51}}=\frac{{25}}{{1326}}\)

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