Two cards. Refers to choosing two cards.
If you do not put the first card back in the deck before you draw the next, what is the probability that the first card is a club and the second card is a diamond? Leave your answer as a fraction in SIMPLEST form.
The probability that the first card is a club and the second card is a diamond is:
(1/4)(13/51)
To solve this problem, we need to break it down into two steps:
Step 1: Finding the probability of drawing a club as the first card.
In a standard deck of 52 playing cards, there are 13 clubs. Therefore, the probability of drawing a club as the first card is 13/52.
Step 2: Finding the probability of drawing a diamond as the second card.
Once the first card has been drawn, there are now 51 cards remaining in the deck, with 13 diamonds. Therefore, the probability of drawing a diamond as the second card, given that the first card was a club, is 13/51.
To find the overall probability, we multiply the probabilities from both steps:
(13/52) * (13/51) = 169/2652
Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor:
169/2652 รท 13/13 = 13/204
Therefore, the probability that the first card is a club and the second card is a diamond, without replacing the first card back in the deck, is 13/204.