a)
P(A) = 4/8 * 3/7 = 3/14 oder auch P(A) = COMB(4, 2)/COMB(8, 2) = 3/14
P(B) = 7/8 * 1/7 * 2 = 1/4
b)
Xi | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
P(Xi) | 2/56 | 2/56 | 4/56 | 4/56 | 6/56 | 6/56 | 8/56 | 6/56 | 6/56 | 4/56 | 4/56 | 2/56 | 2/56 |
P(X ≤ 5) = (2 + 2 + 4)/56 = 1/7
c)
P(1) = 14/56 = 1/4
1 - (1 - 1/4)^n = 0.95 --> n = 10.4 --> Man muss das Experiment mind. 11 mal durchführen.
d)
P(C) = 8/100 * 7/99 = 14/2475 = 0.57%
P(D) = 1 - 14/2475 = 2461/2475 = 99.43%