Question

What is the probability that a five-card poker hand contains the two of diamonds and the three of spades?

(Note: Enter the value in decimal format and report it to four decimal places.)

Answer 1

The probability of getting a five-card poker hand containing the two of diamonds and the three of spades is approximately 0.00005102.

Step-by-step explanation:

To find the probability of getting a five-card poker hand containing the two of diamonds and the three of spades, we need to consider the total number of possible five-card hands and the number of favorable outcomes.

Step 1: Total number of possible five-card hands

In a standard deck of 52 cards, there are C(52, 5) = 2,598,960 different five-card hands.

Step 2: Number of favorable outcomes

The two of diamonds and three of spades can only appear in one specific combination within a five-card hand. There are C(50, 3) = 19,600 different combinations for the other three cards.

Step 3: Calculate the probability

The probability is given by the number of favorable outcomes divided by the total number of possible outcomes. So, the probability is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 1 / 19,600 ≈ 0.00005102

Answer 2

The total probability is 52 choose 5, which is 2598960
Then we multiply the combinations of two diamonds and 3 spades, which is 13 choose 2 times 13 choose 3. That is 22308.
Then we divide to get the decimal. 22308/2598960 is 0.00858343337