Question
Download Solution PDFIn 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
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 0.163Last updated on Jul 9, 2025
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