CBSE 2025, Set 1

Question

**Case Study - 3**
A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective smartphone are only 5%, 4% and 2% respectively. In his inventory he has 25% smartphones from company A, 35% smartphones from company B and 40% smartphones from company C.

A person buys a smartphone from this shop.
(i) Find the probability that it was defective.

Edvaya · Accepted Answer

The correct answer is Subjective. Let $E_1$, $E_2$, and $E_3$ be the events of picking a smartphone manufactured by company A, B, and C respectively. The given probabilities are: $P(E_1) = 25\% = 0.25$ $P(E_2) = 35\% = 0.35$ $P(E_3) = 40\% = 0.40$ Let $D$ be the event that a smartphone is defective. The conditional probabilities are given as: $P(D|E_1) = 5\% = 0.05$ $P(D|E_2) = 4\% = 0.04$ $P(D|E_3) = 2\% = 0.02$ Using the Law of Total Probability, the total probability of picking a defective smartphone $P(D)$ is: $P(D) = P(E_1) \cdot P(D|E_1) + P(E_2) \cdot P(D|E_2) + P(E_3) \cdot P(D|E_3)$ $P(D) = (0.25 	imes 0.05) + (0.35 	imes 0.04) + (0.40 	imes 0.02)$ $P(D) = 0.0125 + 0.0140 + 0.0080$ $P(D) = 0.0345$ The probability that the purchased smartphone is defective is $0.0345$ (or $3.45\%$).

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