Question

in 5 - card poker, the number of outcomes favorable to an event e is given in the table. find the probability of being dealt a royal flush or a straight. the probability of being dealt a royal flush or a straight is (round to 6 decimal places.)

event e	# of outcomes favorable to e
straight flush	36
four of a kind	624
full house	3744
flush	5108
straight	10,200
three of a kind	54,912
two pairs	123,552
one pair	1,098,240
no pair	1,302,540
total	2,598,960

Explanation:

Step1: Find total favorable outcomes

We need to find the number of favorable outcomes for royal flush or straight. From the table, royal flush has 4 outcomes and straight has 10,200 outcomes. So total favorable outcomes = 4 + 10200 = 10204.

Step2: Find total possible outcomes

The total number of 5 - card poker hands is given as 2,598,960.

Step3: Calculate probability

Probability \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{10204}{2598960}\)
First, divide 10204 by 2598960: \( \frac{10204}{2598960}\approx0.003926\) (rounded to 6 decimal places)

Answer:

0.003926