Question

A pair of dice is thrown and sum of the numbers on two tosses is observed. Which of the statements are correct

• A. Probability of getting sum as 11 is \(\frac{1}{18}\)
• B. Probability of getting sum as 5 is \(\frac{1}{12}\)
• C. Probability of getting sum as 7 is \(\frac{1}{6}\)
• D. Probability of getting sum as 6 is \(\frac{1}{9}\)

Answer 1

The Correct Option is A, D

The problem involves calculating the probabilities of different sums when a pair of dice is tossed. There are 6 sides on each die, so there are a total of \(6 \times 6 = 36\) possible outcomes.

Let's analyze each option:

1. Probability of getting sum as 11:
The possible pairs to get a sum of 11 are (5,6) and (6,5). That's 2 favorable outcomes.
Probability \(=\frac{2}{36}=\frac{1}{18}\).

2. Probability of getting sum as 5:
The possible pairs to get a sum of 5 are (1,4), (2,3), (3,2), and (4,1). That's 4 favorable outcomes.
Probability \(=\frac{4}{36}=\frac{1}{9}\), not \(\frac{1}{12}\).

3. Probability of getting sum as 7:
The possible pairs yielding a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). That's 6 favorable outcomes.
Probability \(=\frac{6}{36}=\frac{1}{6}\).

4. Probability of getting sum as 6:
The possible pairs to get a sum of 6 are (1,5), (2,4), (3,3), (4,2), and (5,1). That's 5 favorable outcomes.
Probability \(=\frac{5}{36}\), simplifying gives \(\frac{1}{9}\).

The correct statements are:

• Probability of getting sum as 11 is \(\frac{1}{18}\).
• Probability of getting sum as 6 is \(\frac{1}{9}\).