Consider the set of all possible five-card poker hands dealt fair
Consider the set of all possible five-card poker hands dealt fairly from a standard deck of
fifty-two cards. How many atomic events are there in the joint probability distribution?A. 2, 598, 960
B. 3, 468, 960
C. 3, 958, 590
D. 2, 645, 590
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
A joint probability distribution shows a probability distribution for two or more random variables. It looks for a relationship between two variables say x and y. It gives the probability that each x and y falls in a particular range of set of values specified for that variable.
Explanation:
Here, given:
Total cards = 52
We have to deal with 5 cards.
In this question, atomic events possible can be find in the number of ways they can be combined.
Which is represented as C (n, r) = (n!)/ (n-r)! r!
Here n = 52
r = 5
C (52, 5) = (52)! / (5)! (52 - 5)!
C(52, 5) = \(\frac{{52 \times 51 \times 50 \times 49 \times 48 \times 47!}}{{5 \times 4 \times 3 \times 2 \times 1 \times 47!}}\)
C(52, 5) = 2, 598, 960