SOLUTION: Widgets coming off an assembly line have a 10% defective rate. Five widgets are selected at random and tested. 1.What is the probability that all five of them are defective?

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Question 1047225: Widgets coming off an assembly line have a 10% defective rate. Five widgets are selected at random and tested.

1.What is the probability that all five of them are defective?

2. What is the probability that the first two are defective and the other three are not?

3. What is the probability that the second and fifth ones are defective and the other three are not?

4. How many different outcomes result in exactly two of the five being defective?

5. What is the probability that exactly two of the five are defective?
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Probability all 5 are defective is 0.1^5=0.00001
First two defective is 0.1^2*(0.9)^3=0.00729
The probability is 0.9*0.1*0.9*0.9*0.1=0.00729
The outcomes where 2 are defective is 5C2, or 5!/3!2!, and that is 10
Therefore the probability exactly two are defective is 10*(0.1)^2*(0.9)^3=0.0729.