SOLUTION: The probability that certain production process will produce a defective parts is .20. Find the exact probability that lot of 12 parts will contain a.exactly 5 defective parts b.

Question 1112221: The probability that certain production process will produce a defective parts is .20. Find the exact probability that lot of 12 parts will contain
a.exactly 5 defective parts
b.3 or 4 defective parts
Complete solution please thanks
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Use the binomial probability(P) formula
:
P ( k successes in n trials ) = nCk * p^(k) * (1-p)^(n-k), where nCk = n!/(r! * (n-r)!)
:
a) p=0.20, n=12
:
P ( 5 defects in 12 trials ) = 12C5 * (0.20)^5 * (1-0.20)^(12-5) = 0.0532
:
b) P ( 3 defects in 12 trials ) = 12C3 * (0.20)^3 * (1-0.20)^(12-3) = 0.2362
:
P ( 4 defects in 12 trials ) = 12C4 * (0.20)^4 * (1-0.20)^(12-4) = 0.1329
:
P ( 3 or 4 defects in 12 trials ) = 0.2362 + 0.1329 = 0.3691
:

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