A factory’s quality-check records for two consecutive days are as follows: Day 1…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A factory’s quality-check records for two consecutive days are as follows:
Day 1 production: 120 bulbs, of which 15 were found defective.
Day 2 production: 200 bulbs, of which 32 were found defective.
One bulb is to be selected at random, with equal chance, from the production of the stated day.
(i) For Day 1, find the probability that the bulb selected is defective. Express your answer as a fraction in lowest terms.
(ii) For Day 2, find the probability that the bulb selected is defective. Express your answer as a fraction in lowest terms.
(iii) Compare the results of parts (i) and (ii) to identify on which day selecting a defective bulb is more likely. Support your answer with appropriate reasoning.
(iv) Compute the difference between the two probabilities obtained. Interpret what this difference indicates about the relative quality control performance for the two days.