Question

Two symmetric cubical dice are rolled once. Match the items of Column-I with the items of Column-II. center tabular|l|l|l|l| 2|c|Column-I & 2c|Column-II
A & Probability that the numbers appearing are equal & I & 1/12
B & Probability that the numbers are all distinct & II & 5/36
C & Probability that the sum of numbers is 10 & III & 1/6
D & Probability that the sum of numbers is 6 & IV & 4/36
tabular center

• A. Option 1
• B. Option 2
• C. Option 3
• D. Option 4

Hint:

For sum-based problems with two dice, the number of outcomes for a sum $S$ follows a symmetric pattern: 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1 for sums 2 through 12, respectively.

Answer 1

The Correct Option is B

Concept: When two fair cubical dice are rolled, the total number of possible outcomes is $6 \times 6 = 36$. We calculate the favorable outcomes for each event to find the respective probabilities.

Step 1: Evaluate the probability for event A (numbers are equal).
The favorable outcomes are: $\{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}$.
Number of favorable outcomes $= 6$.
Probability $P(A) = \frac{6}{36} = \frac{1}{6}$. This corresponds to

III.

Step 2: Evaluate the probability for event B (numbers are all distinct).
This is the complement of event A.
Probability $P(B) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}$. This corresponds to

V.

Step 3: Evaluate the probability for event C (sum of numbers is 10).
The favorable outcomes are: $\{(4,6), (5,5), (6,4)\}$.
Number of favorable outcomes $= 3$.
Probability $P(C) = \frac{3}{36} = \frac{1}{12}$. This corresponds to

I.

Step 4: Evaluate the probability for event D (sum of numbers is 6).
The favorable outcomes are: $\{(1,5), (2,4), (3,3), (4,2), (5,1)\}$.
Number of favorable outcomes $= 5$.
Probability $P(D) = \frac{5}{36}$. This corresponds to

II.

Step 5: Map the matches and conclude.
A-III, B-V, C-I, D-II. This matches option (2).
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Correct Match: (B) A-III, B-V, C-I, D-II minipage center