Question

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.

Answer 1

Answer:

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