Theory question 105
ProbabilityBottles of the same sizes produced in a factory are packed in boxes. Each box contains 10 bottles. If 8% of the bottles produced are defective, find correct to two decimal places, the probability that a box chosen at random contains at least three defective bottles.
Show the model answer
Model answer
Binomial: n = 10, p = 0.08, q = 0.92.
P(0) = 0.4344, P(1) = 0.3777, P(2) = 0.1478.
P(X ≥ 3) = 1 − 0.9599 ≈ 0.04.
Explanation
'At least three' = 1 − P(0, 1 or 2).