Final answer:
The binomial probability of pulling exactly 3 aces from a standard deck of cards if you pulled a total of 10 cards is approximately 0.096.
Step-by-step explanation:
To find the binomial probability of pulling exactly 3 aces from a standard deck of cards, we need to consider the number of ways to choose 3 aces out of 4 and the number of ways to choose the remaining 7 cards out of 48.
The probability of drawing an ace is 4/52 for the first card, 3/51 for the second card, and 2/50 for the third card. The probability of drawing a non-ace card is 48/49 for the fourth card, 47/48 for the fifth card, and so on.
Using the binomial probability formula, the probability of pulling exactly 3 aces from 10 cards can be calculated as:
P(3 aces) = C(4,3) * (4/52)^3 * (48/52)^7
Simplifying this expression gives us:
P(3 aces) ≈ 0.096