Question

in 5 - card poker, played with a standard 52 - card deck, $_{52}c_{5}$, or 2,598,960, different hands are possible. the probability of being dealt various hands is the number of different ways they can occur divided by 2,598,960. shown to the right is the number of ways a particular type of hand can occur and its associated probability. find the probability of not being dealt this type of hand.
the probability is (round to six decimal places as needed).

Explanation:

Step1: Recall probability formula

The probability of an event $A$ is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The probability of the complement of an event $A$, denoted as $\overline{A}$, is $P(\overline{A}) = 1 - P(A)$. Here, the total number of 5 - card hands is $n = 2598960$ and the number of a particular type of hand is $m=9764$. So the probability of getting this type of hand is $P(A)=\frac{9764}{2598960}$.

Step2: Calculate the probability of the complement

We want to find the probability of not getting this type of hand, $P(\overline{A})$. Using the formula $P(\overline{A})=1 - P(A)$, we have $P(\overline{A})=1-\frac{9764}{2598960}$.
First, calculate $\frac{9764}{2598960}\approx0.003756$. Then $P(\overline{A})=1 - 0.003756= 0.996244$.

Answer:

$0.996244$