Question

in 6 - card poker, played with a standard 52 - card deck, $_{52}c_6$, or 20,358,520, different hands 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.

number of ways the hand can occur	probability

the probability is \\(\square\\) (round to six decimal places as needed)

Explanation:

Step1: Calculate the probability of getting the hand

The probability of getting the hand is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes is \(7652\) and the total number of outcomes is \(20358520\). So, \(P = \frac{7652}{20358520}\).

Step2: Calculate the probability of not getting the hand

The probability of not getting the hand is \(1 - P\). Substitute \(P=\frac{7652}{20358520}\) into the formula. So, \(1-\frac{7652}{20358520}=\frac{20358520 - 7652}{20358520}=\frac{20350868}{20358520}\).

Step3: Simplify the fraction

\(\frac{20350868}{20358520}\approx0.999624\) (rounded to six decimal places)

Answer:

\(0.999624\)