CA Foundation · Quantitative Aptitude · Probability
A box contains 4 defective and 6 good bulbs. Two bulbs are drawn one after another without replacement. Given that the second bulb is good, what is the probability that the first bulb was defective?
The probability is 4/9. The chance of defective then good is 24/90, and the total chance that the second bulb is good is 54/90. Dividing 24 by 54 gives 4/9. The option 24/90 is only the joint probability and ignores the conditioning.
- A4/10
- B6/9
- C24/90
- D4/9Correct
Explanation
P(first D and second G) = 4/10 x 6/9 = 24/90. P(second G) = (4/10)(6/9) + (6/10)(5/9) = 24/90 + 30/90 = 54/90. Required probability = 24/54 = 4/9. Option 6/9 wrongly treats it as the chance the second is good given the first is defective; 24/90 is the joint probability, not conditional.
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