Question

You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you will have at most three kings in your hand?

Answer 1

To find the probability of having at most three kings in your hand, you need to calculate the probability of getting 0, 1, 2, or 3 kings in the hand and add them together.

Step-by-step explanation:

To find the probability of having at most three kings in your hand, we need to calculate the probability of getting 0, 1, 2, or 3 kings in the hand and add them together.

There are a total of 52 cards in the deck, and 4 of them are kings. So the probability of getting a king on the first draw is 4/52. After the first king is drawn, there are 51 cards left in the deck, including 3 kings. So the probability of getting a king on the second draw is 3/51. Similarly, the probability of getting a king on the third draw is 2/50, and on the fourth draw is 1/49.

To find the probability of getting 0 kings in the hand, we use the formula (48/52)*(47/51)*(46/50)*(45/49)*(44/48). To find the probability of getting 1 king, we use the formula (4/52)*(48/51)*(47/50)*(46/49)*(45/48). And so on for 2 kings and 3 kings.

Finally, we add up the individual probabilities to get the total probability of having at most three kings in the hand.

Answer 2

((4 choose 3)·(48 choose 2) + (4 choose 4)·(48 choose 1)) / (52 choose 5) = 19/10829 = 0.0018