A "flush" in poker is having all the same suit of cards in your poker hand. Remember that a standard deck of cards has 52 cards of four suits: clubs, diamonds, hearts, and spades. Each suit has 13 cards in it. What is the probability that you will be dealt 5 cards of the same suit, resulting in a flush? Express your answer as a decimal rounded to four decimal places. Provide your answer below: \[ P \approx \]

To find the probability of being dealt a flush in poker, we can use combinatorics. First, there are 4 suits to choose from. For each suit, we need to choose 5 cards out of the 13 available in that suit. The number of ways to choose 5 cards from 13 is given by the combination formula \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\). Thus, the number of ways to choose 5 from 13 is: \[ \binom{13}{5} = \frac{13!}{5!(13-5)!} = \frac{13 \times 12 \times 11 \times 10 \times 9}{5 \times 4 \times 3 \times 2 \times 1} = 1287. \] Since there are 4 suits, the total number of ways to get a flush is: \[ 4 \times 1287 = 5148. \] Now, we need to calculate the total number of ways to choose any 5 cards from a standard deck of 52 cards: \[ \binom{52}{5} = \frac{52!}{5!(52-5)!} = \frac{52 \times 51 \times 50 \times 49 \times 48}{5 \times 4 \times 3 \times 2 \times 1} = 2598960. \] Now, the probability \(P\) of getting a flush is the number of flush combinations divided by the total number of combinations: \[ P = \frac{5148}{2598960} \approx 0.001980. \] Rounding to four decimal places: \[ P \approx 0.0020. \]