Question

If you have a 52 card deck:

A) What is the probability  of selecting 2 kings from the deck?

B)   What is the probability of selecting 3 queens?

C) What is the probability of selecting a king, and then an ace, and then a ten?

Thank you.

Answer 1

1. What is the probability  of selecting 2 kings from the deck?

There are 4 kings, the number of way to draw 2 kings are,

4C2   =

The total number of ways to draw 2 cards from a pack of 52 cards is given by,

52C2 =

So the probability of drawing 2 kings is   =

2. What is the probability of selecting 3 queens?

Similarly, we can find probability of selecting 3 queens,

There are 4 queens, the number of ways to draw 3 queens are

4C3 = 4!/(3! *1!)   = 4

The total number of ways to draw 3 cards from pack of 52 cards is given by,

52C3 = 52!/ (3!* 49! ) = 22100

So probability of drawing 3 queens is   4 / 22100 = 0.00018

3. What is the probability of selecting a king, and then an ace, and then a ten?

There are total 52 cards,

There are total 4 kings, 4 ace and 4 ten in standard deck of 52 cards,

Probability of first card drawn a king is 4/52,

Now given that a king is drawn , then there are 51 cards left.

So probability of next card drawn is Ace is 4/51

Now given that a king is drawn and a Ace is drawn , then there are 50 cards left.

So probability of next card drawn is Ten is 4/50.

So required probability is (4/52)*(4/51)*(4/50)   = 64 / 132600    = 0.00048