Question

A game consisting of drawing four cards from a pack of 52 cards without replacement. You win the game if all the cards are the same or if you have three kings or three A. to. Calculate the probability of winning the game. Help with process please!

Answer 1

We want to draw 4 cards from a deck of 52 with no replacement.

The total number of ways of drawing 4 cards is (here, the order of cards is not important)

Let A=event that all cards are the same. There are 13 distinct cards (ignoring the suit). There are 13 ways to draw the first card, after that the rest of the 3 cards have to be the same as the first and hence there is only 1 way to draw the rest.

Number of ways of drawing 4 cards where all cards are the same is

The probability of A is

Let B=event that 3 kings are drawn

There are 4 kings in the deck and 48 other cards. We need to draw 3 kings from the 4 possible and 1 from 48 others

Number of ways of drawing 3 kings is

The probability of B is

Let C=event that 3 As are drawn

There are 4 As in the deck and 48 other cards. We need to draw 3 As from the 4 possible and 1 from 48 others

Number of ways of drawing 3 As is

The probability of C is

We can see that the events, A,B,C do not have any sample elements in common. That is A,B and C are mutually exclusive.

the probability of winning the game is the probability that all the cards are the same or if you have three kings or three A

That is

ans: the probability of winning the game is 0.0015