A factory produces light bulbs in two shifts: the day shift produces 60% of the total daily output and has a defect rate of 2% and the night shift produces the remaining 40% and has a defect rate of 5%. If a randomly selected bulb from the day’s total production is found to be defective, what is the probability that it was produced in the night shift?
(a) 6/8
(b) 1/4
(c) 3/8
(d) 5/8

Question

A factory produces light bulbs in two shifts: the day shift produces 60% of the total daily output and has a defect rate of 2% and the night shift produces the remaining 40% and has a defect rate of 5%. If a randomly selected bulb from the day&rsquo;s total production is found to be defective, what is the probability that it was produced in the night shift?
(a) 6/8
(b) 1/4
(c) 3/8
(d) 5/8

ONLiNE UPSC · Accepted Answer

Assume the factory makes 1000 bulbs per day (to simplify):
Day shift makes 60% of 1000 = 600 bulbs
&rarr; Defective = 2% of 600 = 12 bulbs
Night shift makes 40% of 1000 = 400 bulbs
&rarr; Defective = 5% of 400 = 20 bulbs
Total defective bulbs = 12 (day) + 20 (night) = 32
So, probability that a randomly selected defective bulb came from night shift:
Required Probability = 20/32 = 5/8.
Hence, option d is correct.

Conditional Probability

Defective light bulbs production

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M Question 1	⏱ 0
A factory produces light bulbs in two shifts: the day shift produces 60% of the total daily output and has a defect rate of 2% and the night shift produces the remaining 40% and has a defect rate of 5%. If a randomly selected bulb from the day’s total production is found to be defective, what is the probability that it was produced in the night shift? (a) 6/8 (b) 1/4 (c) 3/8 (d) 5/8