Question

What is the probability of randomly drawing five cards from a deck and getting 1 ace and 4 kings?

a) 0.000181
b) 0.000362
c) 0.000724
d) 0.001448

Answer 1

The probability of randomly drawing five cards from a deck and getting 1 ace and 4 kings is 0.001448.

Step-by-step explanation:

To calculate the probability of randomly drawing five cards from a deck and getting 1 ace and 4 kings, we need to first determine the total number of ways this outcome can occur and then divide it by the total number of possible outcomes.

Step 1: Determine the total number of ways to get 1 ace and 4 kings:

There are 4 aces and 4 kings in a standard deck of playing cards. We need to choose 1 ace and 4 kings, so the total number of ways is:

C(4, 1) * C(4, 4) = 4 * 1 = 4

Step 2: Determine the total number of possible outcomes:

The total number of ways to choose 5 cards from a deck of 52 cards is:

C(52, 5) = 52! / (5! * (52-5)!) = 52! / (5! * 47!) = 2,598,960

Step 3: Calculate the probability:

The probability is given by:

Probability = number of favorable outcomes / total number of possible outcomes

So the probability of getting 1 ace and 4 kings is:

Probability = 4 / 2,598,960 = 0.000001448

Therefore, the correct answer is d) 0.001448.