1) spades x hearts x spades = 13/52 x 13/51 x 12/50 = 3799/5100
2) The primes are 2, 3, 5, 7, 11
2 occurs 1 way (1,1)
3 occurs 2 ways (1,2), (2,1)
5 occurs 4 ways (1,4), (2,3), (3,2), (4,1)
7 occurs 6 ways (1,6), (2,5), (3,4), (4,3), (5,2), (6.1)
11 occurs 2 ways (5,6), (6,5)
There are 15 ways for a prime to be rolled of which 4 have a sum of 5: probability = 4/15
3) a) black x black = 4/9 x 3/8 = 1/6
b) You could get black x black = 4/9 x 3/8 = 1/6
You could get black x white = 4/9 x 5/8 = 5/18
Re-drawing the white and getting a black = 3/8
Combining these two: 5/18 x 3/8 = 5/48
You could get white x black = 5/9 x 4/8 = 5/18
Re-drawing the white and getting a black = 3/8
Combining these two: 5/18 x 3/8 = 5/48
You could get white x white = 5/9 x 4/8 = 5/18
Re-drawing the two white and getting two black = 4/9 x 3/8 = 1/6
Combining these two: 5/18 x 1/6 = 5/108
Adding these possibilities: 1/6 + 5/48 + 5/48 + 5/108 = 89/216