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?
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
The second event, random drawing of a black card from a deck of only 51 remaining cards (event
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:
In our case
After shuffling there are
Let's count only those where there is a red card on the first place and black card on the second.
There are 26 red and 26 black cards. Therefore, we have
Therefore, we have
The final probability, therefore, is
Informative lectures and solutions to many problems of the Theory of Probabilities for beginners can be found in the corresponding chapter on the Web site Unizor (free online course of advanced mathematics for teenagers).