Lot A consist of 3G and 2D articles. Lot B consists of 4G and 1D article, A new lot C is formed by taking 3 articles from A and 2 from B. The probability that an article chosen at random from C is defective, is

Engineering

Mathematics

Basic Definitions Related to Probability

Addition Theorem on Probability

Number of functions

Question

Lot A consist of 3G and 2D articles. Lot B consists of 4G and 1D article, A new lot C is formed by taking 3 articles from A and 2 from B. The probability that an article chosen at random from C is defective, is

$\frac{1}{3}$

$\frac{2}{5}$

$\frac{8}{25}$

none

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P(A) : Event it is chosen from lot A.

$P (A) = \frac{3}{5} P (B) = \frac{2}{5}$

P(Refective) $= P (A) \times P (\frac{D}{A}) + P (B) \times P (\frac{D}{B})$

$= \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{1}{5}$

$= \frac{6}{25} + \frac{2}{25}$

$P (D) = \frac{8}{25}$