A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king. Three cards are randomly drawn without replacement. Calculate the probability of drawing three heart cards. * 3 points 1.5% 2.3% 1.9% 1.3%
To calculate the probability of drawing three heart cards, we first need to determine the total number of ways to draw three cards from a standard deck of 52 cards, and then determine the number of ways to draw three heart cards.
Total number of ways to draw three cards from 52: This can be calculated using the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of cards (52) and r is the number of cards being drawn (3).
C(52, 3) = 52! / [3!(52-3)!] = (52 x 51 x 50) / (3 x 2 x 1) = 22,100
Number of ways to draw three heart cards: Since there are 13 heart cards in a deck, the number of ways to draw three hearts can be calculated using the combination formula.
C(13, 3) = 13! / [3!(13-3)!] = (13 x 12 x 11) / (3 x 2 x 1) = 286
Therefore, the probability of drawing three heart cards is the number of ways to draw three hearts divided by the total number of ways to draw three cards.
Probability = 286 / 22100 ≈ 1.3%
So, the correct answer is 1.3%.