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In a box of 100 bulbs 30 are defective. What is the probability of getting more than 2 defective bulbs if 5 are chosen randomly from the box?

In a box of 100 bulbs 30 are defective. What is the probability of getting more than 2 defective bulbs if 5 are chosen randomly from the box? Correct Answer 0.163

Calculation

Total number of bulbs = 100

Defective bulb = 30

Probability of defective bulb = p = 30/100

⇒ p = 3/10

⇒ q = 1 – p

⇒ q = 1 – 3/10 = 7/10

When 5 bulb are chosen random, n = 5

P(X = x) = ncxpxqn – x

⇒ 5cxpxq5 – x

Getting more than 2 defective bulbs, x = 3, 4, 5

⇒ 5c3(3/10)3(7/10)2 + 5c4(3/10)4(7/10) + 5c5(3/10)5(7/10)5 – 5

⇒ 0.1323 + (5 × 81 × 7)/100000 + (243/100000)

⇒ 0.1323 + 0.02835 + 0.00243

⇒ 0.163

∴ Probability of getting more than 2 defective bulbs if 5 are chosen randomly from the box is 0.163

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