#1
3 black and 2 red balls, total number is 5
i) Both balls are black:
ii) Black and red balls:
#2
22 boys and 18 girls, total number is 40
Combinations of 2 students:
- 40C2 = 40!/38!2! = 40*39/2 = 780
Combination of 2 boys:
- 22C2 = 22!/20!2! = 22*21/2 = 231
Combination of 2 girls:
- 18C2 = 18!/16!2! = 18*17/2 = 153
Probability of selecting 2 students of the same sex:
- P(BB or GG) =
- (231 + 153)/780 =
- 384/780 =
- 96/195 ≈ 0.4923 = 49.23%