[SOLVED] Probability(defective)

Question:
A computer accessories distributor obtains its supply of diskettes from manufacturers A and B, with 60% of the diskettes from manufacture A. The diskettes are packed by the manufacturers in packets of tens. The probability that a diskette produced by manufacturer A is defective is 0.05 whereas the probability that a diskette produced by manufacturer B is defective is 0.02.
Find the probability that a randomly chosen packet contains exactly one defective diskette.

Quote:

Originally Posted by stpmmaths

Question:
A computer accessories distributor obtains its supply of diskettes from manufacturers A and B, with 60% of the diskettes from manufacture A. The diskettes are packed by the manufacturers in packets of tens. The probability that a diskette produced by manufacturer A is defective is 0.05 whereas the probability that a diskette produced by manufacturer B is defective is 0.02. Find the probability that a randomly chosen packet contains exactly one defective diskette.

What a dated problem. One mass storage ‘stick’ stores more the ten packages of disks.
Let D denote that the random chosen pack has exactly one defective disk.
$P(D) = P\left( {D \cap A} \right) + P\left( {D \cap B} \right) = P\left( {D|A} \right)P(A) + P\left( {D|B} \right)P(B)$ .
Now $P\left( {D|A} \right)P(A)=\binom{10}{1}(0.05)(0.95)^9(0.6)$

Can you finsh?

Yes, thanks.