SOLUTION: A diskette manufacturer has determined that 3% of his diskettes are defective. He has just sold 2 disks to a customer. (a) What is the probability that both the disks purchased

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Question 1175643: A diskette manufacturer has determined that 3% of his diskettes are defective.
He has just sold 2 disks to a customer.
(a) What is the probability that both the disks purchased by the customer are
defective?
(b) What is the probability that one of the disks is defective?
I am struggling with what Probability Methods (formulas) to use with these applications. Any help would be greatly appreciated!
Thank You!
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
97% or 0.97 of the disks are not defective
The probability of two in a row not being defective (assuming independence) is 0.97^2=0.9409.
probability that 1 is defective is 2*0.03*0.97=0.0582, since there are two ways that can happen.
The sun of the first two outcomes is 0.9991, and the last possible outcome, that both disks are defective, is 0.03^2 or 0.0009, making the sum 1.0
Answer by ikleyn(53937)   (Show Source): You can put this solution on YOUR website!
.

The formulas and the numbers are


    (a)   P(both defective) = P(1st is defective)*P(2nd is defective) = 0.03*0.03 = 0.0009.      ANSWER


    (b)  P(one of the two is defective) = P(1st is defective)*P(2nd is good) + P(1st is good)*P(2nd is defective) = 

             = 0.03*(1-0.03) + (1-0.03)*0.03 =  0.0582.     ANSWER


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