You are dealt a hand of three cards, one at a time. Find the probability of each of the following. a) The first heart you get is the third card dealt. b) Your cards are all diamonds. c) You get no aces. d) You have at least one heart.

a) 0.145

b) 0.013

c) 0.783

d) 0.586

Step-by-step explanation:

a) there are always 52 cards in total, 13 hearts

Pa = 39/52 * 38/51 * 13/50 = 19266/132600 = 257/1700 = 0.145

b) there are always 13 diamonds in a complete card

Pb = 13/52 * 12/51 * 11/50 = 11/850 = 0.013

c) there are always 4 aces, and 48 that are not aces

Pc = 48/52 * 47/51 * 46/50 = 4324/5525 = 0.783

d) there are 13 hearts, to get at least one heart we have.

Pd = 1 - p

Where p is the probability of no hearts

p = 39/52 * 38/51 * 37/50 = 703/1700 = 0.414

Pd = 1 - 0.414

Pd = 0.586