In the card game bridge, each of 4 players is dealt a hand of 13 of the 52 cards. What is the probability that each player receives exactly one Ace?
Each card has equal probability to end uop in the hand of the different players. So, for each ace you have 4 equaly likely choices for the players they will end up at, there are thus 4^4 = 2^8 ways the aces can end up in the hands of the players.
There are 4! ways to distribute the four aces over the 4 persons such that each person gets one ace. The probability of this happening is thus:
4!/2^8 = 3/2^5 = 3/32
it is wrong
To calculate the probability that each player receives exactly one Ace in the card game bridge, we need to determine the number of favorable outcomes and the total number of possible outcomes.
To start, let's find the number of favorable outcomes, which is the number of ways each player can receive exactly one Ace.
First, we need to find the number of ways to pick one Ace out of four available Aces and give it to the first player. This can be calculated using the combination formula, denoted as C(n, r), where n is the total number of items and r is the number of items being chosen. In this case, n = 4 (number of Aces) and r = 1 (number of Aces to be assigned to the first player). So the number of ways to give one Ace to the first player is C(4, 1) = 4.
Next, after the first player has received one Ace, there are 3 Aces left. We now need to find the number of ways to give one Ace to the second player out of the remaining 3 Aces. Again, using the combination formula, C(3, 1) = 3.
We repeat this process for the third player, giving one Ace to them out of the remaining 2 Aces (C(2, 1) = 2).
Finally, for the fourth player, we are left with only one Ace, so there is only one way to assign it.
To calculate the total number of possible outcomes, we need to find the number of ways to distribute the 52 cards among the 4 players. This can be calculated using the permutation formula, denoted as P(n, r), where n is the total number of items and r is the number of items being arranged. In this case, n = 52 (total number of cards) and r = 13 (cards to be given to each player). So the total number of possible outcomes is P(52, 13) * P(39, 13) * P(26, 13) * P(13, 13).
Now, we can calculate the probability by taking the number of favorable outcomes divided by the total number of possible outcomes:
Probability = (4 * 3 * 2 * 1) / (P(52, 13) * P(39, 13) * P(26, 13) * P(13, 13))
After evaluating this expression, we can determine the probability that each player receives exactly one Ace in the card game bridge.