Probability question help

In summary, probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. Theoretical probability is based on mathematical calculations, while experimental probability is based on observations or experiments. To calculate probability, divide the number of favorable outcomes by the total number of possible outcomes. Independent events do not affect each other, while dependent events are influenced by each other. The multiplication rule in probability states that the probability of two independent events occurring together is equal to the product of their individual probabilities.
  • #1
tc
7
0
how to solve it..
what is the probability that each player has a hand containing an ace when the 52 cards of a standard deck are dealt to four players?
 
Mathematics news on Phys.org
  • #2
tc said:
how to solve it..
what is the probability that each player has a hand containing an ace when the 52 cards of a standard deck are dealt to four players?

The probability that the first person gets one ace * the probability of the second...

IE how likely is it that a player gets exactly on ace in 13/52 cards? How likely for 13/(52-13)? etc..
 
  • #3


To solve this probability question, we need to first determine the total number of possible hands that can be dealt from a standard deck of 52 cards. This can be calculated using the formula for combinations, which is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. In this case, n = 52 and r = 13 (since there are 13 possible cards that could be an ace). So the total number of possible hands is 52C13 = 635,013,559,600.

Next, we need to determine the number of possible hands that contain an ace for each player. Since there are 4 players, we need to calculate this for each player separately. The first player has a 4/52 chance of getting an ace (since there are 4 aces in a deck of 52 cards). The second player has a 3/51 chance of getting an ace (since there are now 3 aces left in a deck of 51 cards). The third player has a 2/50 chance of getting an ace, and the fourth player has a 1/49 chance of getting an ace. To get the total number of possible hands with an ace for each player, we multiply these probabilities: (4/52) * (3/51) * (2/50) * (1/49) = 0.0000000000000000039.

Finally, to find the probability that each player has a hand containing an ace, we divide the number of possible hands with an ace for each player by the total number of possible hands: 0.0000000000000000039 / 635,013,559,600 = 0.0000000000000000000000061. This means that the probability that each player has a hand containing an ace is 0.0000000000000000000000061 or approximately 0.00000000000000000000061%.
 

What is probability?

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

What is the difference between theoretical and experimental probability?

Theoretical probability is the likelihood of an event occurring based on mathematical calculations, while experimental probability is based on actual observations or experiments.

How do you calculate probability?

To calculate probability, divide the number of favorable outcomes by the total number of possible outcomes. This can be represented as P(event) = number of favorable outcomes / total number of possible outcomes.

What is the difference between independent and dependent events?

Independent events are events that do not affect each other, while dependent events are events that are influenced by each other.

How do you use the multiplication rule in probability?

The multiplication rule states that the probability of two independent events occurring together is equal to the product of their individual probabilities. It can be represented as P(A and B) = P(A) x P(B).

Similar threads

  • General Math
Replies
6
Views
322
  • General Math
Replies
1
Views
2K
Replies
9
Views
2K
  • General Math
Replies
4
Views
1K
  • General Math
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
31
Views
2K
Replies
17
Views
2K
  • General Math
Replies
4
Views
2K
  • General Math
Replies
1
Views
692
Back
Top