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. the probability is □ (round to six decimal places as needed.) number of ways the hand can occur 7652 probability $\frac{7652}{20358520}$

Explanation:

Step1: Recall probability formula

The probability $P$ of an event is given by $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The probability of being dealt a particular hand is $p_1=\frac{7652}{20358520}$.

Step2: Calculate probability of not - being dealt the hand

The probability of not being dealt the hand, $p_2$, is given by $p_2 = 1 - p_1$. First, calculate $p_1=\frac{7652}{20358520}\approx0.0003758$. Then $p_2=1 - 0.0003758 = 0.9996242$.

Answer:

$0.999624$