Question

Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then.
Match List I with List II.

List I	List II
A. P (X = 2)	I. \(\frac{4}{36}\)
B. P (X = 4)	II. \(\frac{5}{36}\)
C. P (X - 5)	III. \(\frac{1}{36}\)
D. P (X - 6)	IV. \(\frac{3}{36}\)

Choose the correct answer from the options given below:

• A. А-I, В-II, С-III, D-IV
• B. А-II, В-III, С-IV, D-I
• C. A-III, B-IV, C-I, D-II
• D. A-IV, B-I, C-II, D-III

Answer 1

The Correct Option is C

A pair of dice can be thrown to get various sums ranging from 2 to 12. The random variable X represents this sum. We will calculate the probabilities for these sums and match them with the options provided in List II.

• P(X=2): This occurs only when both dice show 1, i.e., (1,1). The probability is thus \( \frac{1}{36} \).
• P(X=4): The combinations are (1,3), (2,2), and (3,1). The probability is \( \frac{3}{36} \).
• P(X=5): The combinations are (1,4), (2,3), (3,2), and (4,1). The probability is \( \frac{4}{36} \).
• P(X=6): The combinations are (1,5), (2,4), (3,3), (4,2), and (5,1). The probability is \( \frac{5}{36} \).

List I	List II
A. P(X=2)	III. \(\frac{1}{36}\)
B. P(X=4)	IV. \(\frac{3}{36}\)
C. P(X=5)	I. \(\frac{4}{36}\)
D. P(X=6)	II. \(\frac{5}{36}\)

Thus, the correct matching is A-III, B-IV, C-I, D-II.