A card is drawn from a standard deck. A second card is drawn, without replacing the first card. What is the probability that the first card is red and the second card is black?

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Clark Carson · Accepted Answer

In the standard deck of cards there are 52 cards, 26 red and 26 black.  The first event, random drawing of a red card (event A), has a sample space of an entire deck with 52 different elementary events occurring with equal probabilities of 152. Out of them only 26 events are &quot;good&quot; (that is, the card we randomly pick is red). Therefore, the probability of picking a red card equals to P(A)=2652=12.  The second event, random drawing of a black card from a deck of only 51 remaining cards (event B), is dependent on the results of the first event. If the first event (event A) occurs (red card is drawn), the deck for the second drawing contains 25 red and 26 black cards and the conditional probability of picking black card is P(B∣A)=2651.  Now we can use the concept of conditional probability and a formula that describes the probability of a combined event through the probability of one and conditional probability of another:  P(A⋅B)=P(A)⋅P(B∣A)  In our case P(A)=12 and P(B∣A)=2651  Therefore, P(A⋅B)=(12)⋅(2651)=1351

Bryce Barry · Accepted Answer

After shuffling there are 52! permutations of 52 cards. Each has the probability of occurrence equal to another, that is the probability of any sequence of cards is 152!  Lets

A card is drawn from a standard deck. A second

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