5 cards are drawn at random from standard deck find the probability that all cards are hearts
There are 13 hearts in a standard deck of 52 cards. Therefore, the probability of drawing a heart on the first draw is 13/52. Since the cards are drawn without replacement, the probability of drawing a heart on the second draw, given that a heart was drawn on the first draw, is 12/51. Similarly, the probabilities for the third, fourth, and fifth draws are 11/50, 10/49, and 9/48, respectively.
To find the probability of drawing all hearts, we need to multiply the probabilities of each draw together, since each draw is independent:
(13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.000495 or approximately 0.05%
Therefore, the probability of drawing 5 hearts in a row is very low - about 1 in 2020.