What is the probability that a five-card poker hand contains a flush (including straight and royal flushes), that is, five cards of the same suit? (Enter the value of probability in decimals. Round the answer to five decimal places.)

0.00198

Step-by-step explanation:

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

⁵²C₅ = 2,598,960 ways.

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

Note that of the 52 cards, each suit has 13 cards, So, ⁴C₁ represents selecting a suit out of 4 different suits and ¹³C₅ represents selecting 5 cards out of 13 cards thay a suit contains.

So, the probability of a flush

= 5148 ÷ 2,598,960 = 0.0019807923 = 0.00198 to 5 d.p

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step-by-step explanation: