How did the value for probability of A given B come about at bottom here? I have no idea how that equation was generated.
This problem is solved in the chapter before distributions of discrete random variable. The section deals with Bayes' Rule.
Is there a manner to generate the same equation without a known distribution at hand?
- PuzzlingLv 72 years agoFavorite Answer
A is the event that 1 of the 3 fuses was defective
B is the event that the fuses came from line 1
If the fuse came from line 1 (given as B), then we only have to consider those probabilities. We use the binomial probability:
P(X=k) = C(n,k) * p^k * q^(n-k)
n : number of total fuses tested (3)
k : number of defective fuses (1)
p : probability it is defective (0.05)
q : probability it is not defective (0.95)
P(X=1) = C(3,1) * 0.05 * 0.95²
= 3 * 0.05 * 0.95²
Basically the 3 comes from the number of ways to pick which of the 3 is the defective fuse.
The probability of one being defective is 0.05
The probability of two more being non-defective is 0.95²