a. You replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is also 13/52 or 1/4. And the probability of drawing a heart on the third draw is also 13/52 or 1/4.
Since the events are independent, we can multiply the probability of each event to find the probability that all three cards are hearts: (1/4) * (1/4) * (1/4) = 1/64.
b. You do not replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is 12/51 since we already drew a heart before, the total number of cards left in the deck is 51. The probability of drawing a heart on the third draw is 11/50 since we already drew 2 hearts before, the total number of cards left in the deck is 50.
The probability that all three cards are hearts is (1/4) * (12/51) * (11/50) = 0.0217 or approximately 2.17%.
It's important to note that in the first case the probability of drawing a heart on the second and third draw is still 1/4 because we are replacing the cards back before drawing the next one, so all 52 cards are available again. While on the second case, we don't replace the cards back and that's why the probability of drawing a heart on the second and third draw is different.Answer:
Explanation: