Question

You are dealt a hand of three​ cards, one at a time. Find the probability of each of the following.

​a) The first red card you get is the third card dealt.

​b) Your cards are all hearts.

​c) You get no clubs.

​d) You have at least one king.

Answer 1

Combination formula: nCr = n!/(r! x (n-r)!)

a) Number of red cards = 26

Number of black cards = 26

P(the first red card you get is the third card dealt) = P(first 2 cards are black) x P(third card from remaining 50 is red)

= 26/52 x 25/51 x 26/50

= 0.12745

b) Number of hearts = 13

P(all are hearts) = 13C3 / 52C3

= 286/22,100

= 0.01294

c) Number of non-clubs = 52 - 13 = 39

P(no clubs) = 39C3/52C3

= 0.41353

d) Number of kings = 4

Number of non-kings = 52 - 4 = 48

P(at least one king) = 1 - P(no kings)

= 1 - 48C3/52C3

= 1 - 0.78562

= 0.21738