A factory classifies each bulb it produces into exactly one of the following quality…
MATHEMATICS · Subjective · CBSE · Mathematics · Probability · Probability
Problem
A factory classifies each bulb it produces into exactly one of the following quality grades:
Grade A : 45 % of the day’s production
Grade B : 25 % of the day’s production
Grade C : 18 % of the day’s production
Grade D : the remaining bulbs (which are still saleable but of the lowest grade)
A bulb is selected at random from that day’s production.
(i) Explain why the four quality grades A, B, C and D form a set of mutually exclusive and exhaustive events.
(ii) Find the percentage of bulbs that are graded D.
(iii) Express the given percentages as probabilities for grades A, B, C and D.
(iv) Calculate the probability that the selected bulb is either Grade B or Grade C.
(v) Verify that the sum of the probabilities of the four grades is 1, thereby confirming the probability axiom for this classification.