a hand consists of 4 cards from a well - shuffled deck of 52 cards. a. find the total number of possible 4…

a hand consists of 4 cards from a well - shuffled deck of 52 cards. a. find the total number of possible 4 - card poker hands. b. a black flush is a 4 - card hand consisting of all black cards. find the number of possible black flushes. c. find the probability of being dealt a black flush. a. there are a total of 270725 poker hands. b. there are 14950 possible black flushes. c. the probability is . (type an integer or decimal rounded to six decimal places as needed.)

a hand consists of 4 cards from a well - shuffled deck of 52 cards. a. find the total number of possible 4 - card poker hands. b. a black flush is a 4 - card hand consisting of all black cards. find the number of possible black flushes. c. find the probability of being dealt a black flush. a. there are a total of 270725 poker hands. b. there are 14950 possible black flushes. c. the probability is . (type an integer or decimal rounded to six decimal places as needed.)

Answer

Explanation:

Step1: Recall probability formula

Probability $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes.

Step2: Identify values

We know from part a that $n(S) = 270725$ (total number of 4 - card hands) and from part b that $n(A)=14950$ (number of black flushes).

Step3: Calculate probability

$P=\frac{14950}{270725}=\frac{2990}{54145}\approx 0.055222$

Answer:

$0.055222$