Compute the Probability of an Event Using the Complement Rule
-In 5 -card poker, played with a standard 52 -card deck, 2,598,960 different hands are possible. If there are 624 different ways a "four-of-a-kind" can be dealt, find the probability of not being dealt a "four-of-a-kind".
A) $\frac { 2,598,336 } { 2,598,960 }$
B) $\frac { 624 } { 2,598,960 }$
C) $\frac { 625 } { 2,598,960 }$
D) $\frac { 1248 } { 2,598,960 }$

Question

Quizplus · Accepted Answer

The probability of not being dealt a "four-of-a-kind" is found by subtracting the probability of being dealt a "four-of-a-kind" from 1. Since there are 624 ways to get a "four-of-a-kind" out of 2,598,960 possible hands, the probability of getting a "four-of-a-kind" is $ \frac{624}{2,598,960} $. Thus, the probability of not getting a "four-of-a-kind" is $ 1 - \frac{624}{2,598,960} = \frac{2,598,960 - 624}{2,598,960} = \frac{2,598,336}{2,598,960} $.

Compute the Probability of an Event Using the Complement Rule 2,598,3362,598,960\frac { 2,598,336 } { 2,598,960 }2,598,9602,598,336​

Compute the Probability of an Event Using the Complement Rule $\frac { 2,598,336 } { 2,598,960 }$