For this problem, assume that youre dealt 5 cards from a standard .pdf

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This document discusses the probability of drawing certain card combinations from a standard 52-card deck. It provides the solutions to two probability problems: (a) Drawing 2 clubs, 2 hearts, and 1 diamond, which has a probability of 0.03. (b) Getting 2 pairs with one red and one black, which has a probability of 0.003. The work shown uses combinations and considers the number of possible combinations for drawing the specified cards compared to the total number of combinations for drawing 5 cards from the deck.

Formation

For this problem, assume that you're dealt 5 cards from a standard deck of 52 cards.
(a) What is the probability of drawing 2 clubs, 2 hearts, and 1 diamond?
(b) What is the probability of getting 2 pairs, one red and the other black?
show work
Solution
a) there are 13 clubs no of ways 2 clubs can be drawn = 13C2 similarly for hearts
also and no of ways 1 diamond can be drawn from total 13 diamonds = 13C1 Total no of ways 5
cards can be drawn = 52C5 probability of drawing 2 clubs, 2 hearts, and 1 diamond = 13C2 *
13C2 * 13C1 / 52C5 = .03 b) here we have to get a red pair and black pair there are 13 red pairs
and 13 black pairs we have to chose 1 from 5th card can be anything from remaining 48 cards so
the probability of getting 2 pairs, one red and the other black = 13C1 * 13C1 * 48C1 / 52C5 =
.003

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