Math, asked by Manasi3902, 2 months ago

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

Answers

Answered by Harshitpro123

Step-by-step explanation:

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Answered by amitnrw

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