Final answer:
To determine the probability of drawing three aces without replacement from a standard deck, multiply the probabilities of drawing an ace at each step: (4/52) * (3/51) * (2/50).
Step-by-step explanation:
The question asks for the probability of drawing three aces in a row without replacement from a standard 52-card deck. To calculate this, we use the multiplication rule for independent events. To calculate the probability of drawing 3 aces from a standard 52-card deck without replacement, we need to consider the number of ways to draw 3 aces and the total number of possible combinations when drawing 3 cards without replacement.The number of ways to draw 3 aces from a deck is given by choosing 3 aces out of the 4 available:C(4, 3) = 4
The total number of possible combinations when drawing 3 cards without replacement is given by choosing 3 cards out of the 52 available:Initially, there are 4 aces out of 52 cards. The probability of drawing an ace on the first draw is therefore 4/52 (or 1/13). After drawing one ace, there are now 3 aces left and only 51 cards remaining in the deck. Consequently, the probability of drawing another ace is now 3/51. For the third card, the deck has only 50 cards left with 2 aces among them, making the probability of drawing an ace 2/50. The total probability of drawing three aces consecutively without replacement is obtained by multiplying these probabilities together: (4/52) * (3/51) * (2/50).