Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Two dice are thrown. Probability that the sum is 8, given that both numbers are even | (I) | \(\displaystyle\frac{4}{7}\) |
| (B) | A die is thrown. Probability that the number is greater than 3, given that it is even | (II) | \(\displaystyle\frac{1}{12}\) |
| (C) | P(A|B), where P(A) = 0.5, P(B) = 0.35 and P(B|A) = 0.4 | (III) | \(\displaystyle\frac{1}{3}\) |
| (D) | A coin is tossed and a die is thrown. Probability of a head on the coin and a 6 on the die | (IV) | \(\displaystyle\frac{2}{3}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A) Two dice are thrown. Probability that the sum is 8, given that both numbers are even
This matches (III) \(\frac{1}{3}\).
Each die can show 2, 4 or 6, so the condition leaves a reduced sample space of \(3\times 3 = 9\) outcomes. Of these, (2, 6), (4, 4) and (6, 2) have sum 8:
\( \displaystyle P = \frac{3}{9} = \frac{1}{3} \)
(B) A die is thrown. Probability that the number is greater than 3, given that it is even
This matches (IV) \(\frac{2}{3}\).
The even numbers are 2, 4, 6. Of these, 4 and 6 are greater than 3:
\( \displaystyle P = \frac{2}{3} \)
(C) P(A|B), where P(A) = 0.5, P(B) = 0.35 and P(B|A) = 0.4
This matches (I) \(\frac{4}{7}\).
By the multiplication theorem:
\(P(A\cap B) = P(A)\,P(B|A) = 0.5\times 0.4 = 0.2\)
\( \displaystyle P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{0.2}{0.35} = \frac{4}{7} \)
(D) A coin is tossed and a die is thrown. Probability of a head on the coin and a 6 on the die
This matches (II) \(\frac{1}{12}\).
The coin and the die do not affect each other, so the events are independent:
\( \displaystyle P = \frac{1}{2}\times\frac{1}{6} = \frac{1}{12} \)