Question

jeweller while fitting a gem breaks it 2% of the times.If he works on 100 stones,what is the probability of breaking at least 3 stones?( hint: round off three decimal places)
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Answer 1

Given:

The jeweler breaks a gem while fitting it 2% of the times.

To find:

If the jeweler works on 100 stones, what is the probability of breaking at least 3 stones?

Solution:

Probability that the jeweler breaks the gem = 2/100 = 0.02

Probability of not breaking the gem = 1-0.02 = 0.98

Using the binomial expansion: ⁿCₓ pˣ q ⁿ⁻ˣ

The probability of breaking at least 3 stones P(at least 3)= 1 - P(0) - P(1) - P(2)

= 1- ¹⁰⁰C₀ (0.02)⁰ (0.98)¹⁰⁰ - ¹⁰⁰C₁(0.02)¹ (0.98)⁹⁹ - ¹⁰⁰C₂ (0.02)²(0.98)⁹⁸

= 1 - 0.1326 - 0.2679 - 0.2734

= 1 - 0.6739

= 0.3261 ≈ 0.326

Therefore the required probability is 0.326.