There are 4 Aces in a standard deck, and there are 48 non-Ace cards
The probability of not drawing an Ace in the first draw is (48/52).
The probability of not drawing an Ace in the second draw, after not drawing one in the first, is (47/51).
The probability of not drawing an Ace in the third draw, after not drawing one in the first and second, is (46/50).
Now, multiply these probabilities together:
$p= (48/52) \cdot (47/51) \cdot (46/50)$
This is the probability of not drawing any Aces in all three draws. To find the probability of drawing at least one Ace, subtract this from 1:
$1 - p$
Now, to calculate the probability of drawing 3 cards of the same suit (Hearts, Diamonds, Spades, or Clubs), you can use the following approach:
- Calculate the probability of drawing 3 cards of the same suit (e.g., Hearts).
- Multiply this probability by 4 (since there are 4 suits in a standard deck) to account for all possible suits.
So,
$p= 4\cdot (13/52) \cdot (12/51) \cdot (11/50)$
This is because there are 13 cards of each suit in a standard deck, and we’re calculating the probability of drawing one from that suit on each of the three draws.