4 cards are drawn at random (without replacement) from a pack of 52 cards. Find the probability that, 2 are black and 2 are red. (Enter the answer correct to two decimal places)
Question
4 cards are drawn at random (without replacement) from a pack of 52 cards. Find the probability that, 2 are black and 2 are red. (Enter the answer correct to two decimal places)
Solution
The total number of ways to draw 4 cards out of 52 is given by the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, the total number of ways to draw 4 cards out of 52 is C(52, 4).
The number of ways to draw 2 black cards from 26 black cards is C(26, 2), and the number of ways to draw 2 red cards from 26 red cards is C(26, 2).
So, the total number of favorable outcomes is C(26, 2) * C(26, 2).
The probability of drawing 2 black and 2 red cards is then given by the number of favorable outcomes divided by the total number of outcomes, or [C(26, 2) * C(26, 2)] / C(52, 4).
Let's calculate these values:
C(52, 4) = 52! / [4!(52-4)!] = 270725 C(26, 2) = 26! / [2!(26-2)!] = 325 So, [C(26, 2) * C(26, 2)] = 325 * 325 = 105625
Therefore, the probability is 105625 / 270725 = 0.39 (rounded to two decimal places).
Similar Questions
Four cards are drawn, without replacement, from a deck of 52 cards. Write the probability distribution for the number of red cards drawn
Select the correct answerIn a rummy game, 3 cards are drawn from a pack of 52 cards. What is the probability that all the three cards are of red colour?
What is the probability of drawing a red card in a standard deck of 52 cards? (Enter your probability as a fraction.)
Two cards are drawn in order without replacement from a regular deck of 52 cards.Write all answers as simplified fractions.What is the probability the first card is a heart? What is the probability the second card is a red card given the first card was a heart? What is the probability the first card is a heart and the second card is a red?
If 2 cards are selected from a standard deck of cards. The first card is placed backin the deck before the second card is drawn. Find the probability of getting:A red card and 4 of spades (in exact order)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.