SOLUTION: 3. From experience, a battery manufacturer knows the probability of a battery being defective is .08. If a retail customer buys four batteries, what is the probability that all of
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Question 312098: 3. From experience, a battery manufacturer knows the probability of a battery being defective is .08. If a retail customer buys four batteries, what is the probability that all of the batteries are defective?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need to calculate the probability of 
successes in 
trials where the probability of success on any given trial is 
.
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of ways to select things from things where order doesn't matter, i.e. !})
For this particular problem 
, 
, and 
\ =\ \frac{4!}{4!(0)!}\ =\ 1)
\ =\ \left(1\right\)\(0.08)^4\left(0.92\right)^{0}\ \approx\ 0.000041)
Certainly less precise, but also certainly more illustrative, would be to say, "about a snowball's chance in hell."
John
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