Question

The probability that a pen manufactured by a company will be defective is 1/10. If 12 such pens are manufactured, find the probability that​

Answer 1

Probability that Exactly two will be defective  is about 0.23

Probability that  at least two will be defective  is about 0.341

Given:

• Probability of defective pen = 1/10
• 12 Such Pens manufactured

To Find:

• Probability that
• (i) exactly two will be defective
• (ii) at least two will be defective

Solution:

P(x) = ⁿCₓpˣ(1-p)ⁿ⁻ˣ

n = 12

p = 1/10

1 - p = 1- 1/10  = 9/10

Step 1:

Probability that Exactly two will be defective  P(2)

P(2) = ¹²C₂(1/10)²(9/10)¹²⁻²

P(2) = 66 * 9¹⁰ / 10¹²

P(2) ≈ 0.23

Step 2:

Probability that  at least two will be defective  1 - P(0) - P(1)

P(0) = ¹²C₀(1/10)⁰(9/10)¹²⁻⁰

P(1) =  ¹²C₁(1/10)¹(9/10)¹²⁻¹

1 - P(0) - P(1) ≈ 0.341

Probability that Exactly two will be defective  is about 0.23

Probability that  at least two will be defective  is about 0.341

( Although your Question is Incomplete , probably you are referring to the below Question)

(i) exactly two will be defective (ii) at least two will be defective

https://brainly.in/question/39342899