Question

A manufacturing machine has a 6% defect rate. If 6 items are chosen at random, what is the probability that atleast one will have the defect?

Answer 1

Answer:

6 percent defect rates means out of 100 , 6 are defected .

Means 94 are undefected and good.

Now , P( 100) = 6

hence , P ( 1 ) = 1 / 94 .

Hence , Probabiltity for Simultaneous Occurence must be

( 1/94 ) ^ 6 = 1 / 689869781056

Answer 2

A manufacturing machine has a 6% defect rate. If 6 items are chosen at random.

We have to find the probability of at least one defect.

Probability of defective item, P(defective) = 6 % = 0.06

Probability of non-defective item, P(non-defective) = 1 - P(detective) = 1 - 0.06 = 0.94

Binomial distribution formula :

$P(x\geq1)=1-^nC_r(P)^r(1-P)^{(n-r)}$

• n = number of trials
• r = number of success desired
• P = probability of getting success in one trial.
• 1 - P = Probability of not getting success in one trial.

Here, P = 0.06 , 1 - P = 0.94 , n = 6 , r = at least one defect i.e., r < 1 (means, r ≤ 0 or, r = 0)

∴ P(x≥1) = 1- ⁶C₀ × (0.06)⁰ × (0.94)⁶

= 1 - 1 × 1 × 0.689869781 ≈ 0.31

Therefore the probability of getting at least one defect is 0.31