a)
P(X < 3) = ∑(COMB(100, x)·0.05^x·0.95^(100 - x), x, 0, 3) = 25.78%
μ = n·p = 100·0.05 = 5
σ = √(n·p·(1 - p)) = √(100·0.05·0.95) = 2.179
b)
P(X = 2) = COMB(2, 2)·COMB(48, 3)/COMB(50, 5) = 0.82%
c)
. | Defekt | Heil | . |
Verkauf | 0.00025 | 0.94715 | 0.9474 |
Nicht Verkauf | 0.04975 | 0.00285 | 0.0526 |
. | 0.05 | 0.95 | 1 |
P(Defekt | Verkauf) = 0.00025/0.9474 = 0.026%