Probability?

Question

In a game of chance, 2 cards are drawn at random from a pack of playing cards without replacement. An ace has a value of 1 and all picture cards have a value of 10 each.

What is the probability of

(i) drawing 2 picture cards,

(ii) drawing 2 cards having the same picture (that is 2 kings or 2 queens or 2 jacks).

(iii) the cards drawn having a total value of 18


Please show your steps clearly..

Answer 1

q1
12 picture cards in a deck of 52

P=12C2/52C2
=12*11/52*51
=11/221

q2
4K, 4Q, 4J

P=3 * 4C2/52C2
=3*4*3/52*51
=3/221

q3
18=10+8=9+9
12 10s(pictures) and 4 8s
or 4 9s

P=[12C1*4C1 + 4C2]/52C2
=(48+6)/26*51
=54/26*51
=9/13*17
=9/221

Answer 2

Assuming a 52-card pack:
(i) drawing 2 picture cards,
p = (12/52)(11/51)
p = (1/13)(11/17)
p = 11/221 ≈ 0.04977376

(ii) drawing 2 cards having the same picture (that is 2 kings or 2 queens or 2 jacks
p = (12/52)(3/51)
p = (3/13)(1/17)
p = 3/221 ≈ 0.01357466

(iii) the cards drawn having a total value of 18
p = (16/52)(4/51) + (4/52)(16/51) + (4/52)(3/51)
p = (24/52)(23/51)
p = (2/13)(23/17)
p = 46/221
p = 0.20814480