Question

in 6 - card poker, played with a standard 52 - card deck, 52c6 different ways are possible. the probability of being dealt various hands is the number of different ways they can occur divided by 20,358,520. 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 $A$ occurring is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The probability of the complement of an event $A$ (not - $A$) is $P(\text{not }A)=1 - P(A)$.

Step2: Calculate $P(A)$

We are given that the number of ways a particular hand can occur is $62$ and the total number of possible 6 - card hands is $20358520$. So $P(A)=\frac{62}{20358520}$.

Step3: Calculate $P(\text{not }A)$

$P(\text{not }A)=1-\frac{62}{20358520}=\frac{20358520 - 62}{20358520}=\frac{20358458}{20358520}\approx0.999997$.

Answer:

$0.999997$