Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | A coin is tossed. On a head a ball is drawn at random from Bag I (1 white, 1 black ball), and on a tail from Bag II (2 white balls). Probability that the ball is white | (I) | \(\displaystyle\frac{7}{24}\) |
| (B) | A die is thrown. If it shows 6, a ball is drawn at random from Box I (1 red, 1 blue ball); otherwise from Box II (1 red, 3 blue balls). Probability that the ball is red | (II) | \(\displaystyle\frac{1}{2}\) |
| (C) | Machine M produces 40% of the items of a factory, of which 5% are defective; machine N produces the rest, of which 10% are defective. Probability that an item chosen at random is defective | (III) | \(\displaystyle\frac{3}{4}\) |
| (D) | Of the players of a quiz, \(\frac{1}{3}\) are adults and \(\frac{2}{3}\) are children. An adult answers a question correctly with probability \(\frac{3}{4}\) and a child with probability \(\frac{3}{8}\). Probability that a player chosen at random answers correctly | (IV) | \(\displaystyle\frac{2}{25}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
Each item uses the theorem of total probability: multiply the chance of each case by the chance of the result in that case, and add.
(A) Coin decides the bag; probability that the ball is white
This matches (III) \(\frac{3}{4}\).
\( \displaystyle P = \frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times 1 = \frac{1}{4}+\frac{1}{2} = \frac{3}{4} \)
(B) Die decides the box; probability that the ball is red
This matches (I) \(\frac{7}{24}\).
\( \displaystyle P = \frac{1}{6}\times\frac{1}{2}+\frac{5}{6}\times\frac{1}{4} = \frac{2}{24}+\frac{5}{24} = \frac{7}{24} \)
(C) Two machines; probability that an item is defective
This matches (IV) \(\frac{2}{25}\).
\( P = 0.4\times 0.05+0.6\times 0.10 = 0.02+0.06 = 0.08 \)
\( \displaystyle 0.08 = \frac{8}{100} = \frac{2}{25} \)
(D) Adults and children; probability of a correct answer
This matches (II) \(\frac{1}{2}\).
\( \displaystyle P = \frac{1}{3}\times\frac{3}{4}+\frac{2}{3}\times\frac{3}{8} = \frac{1}{4}+\frac{1}{4} = \frac{1}{2} \)