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Draw 4 cards from a deck. Determine the probability that all of them are hearts. Will it be 1/13 * 1/12 * 1/11 * 1/10 ? I'm not sure, any help will be helpful, thanks!
Sarah J. what is the probability of drawing four hearts in a row from a standard deck when the drawn card is returned to the deck each time 2 Answers By Expert Tutors
There are 13 hearts in a deck of 52 cards So the probality of drawing a heart is 1/4 since you return the card to the deck this does not change from draw to draw therefore the probability of drawing four in a row would be or about .39% (less than 1%
There are 13 hearts in a 52 card deck, 13/52 = 1/4. So if you replace the card, the probability of picking a heart on any draw is 1/4. The probability of picking a heart on 4 consecutive draws is: (1/4)(1/4)(1/4)(1/4) = (1/4)4 = 1/256 = 0.390% If you don't return the card, you have one less card and one less heart on each successive draw. So the probability on the first draw is 1/4, but it reduces to 12/51 on the second draw, 11/50 on the third draw, and 10/49 on the fourth draw. (1/4)(12/51)(11/50)(10/49) = 0.264% |