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 \(\displaystyle\frac{1}{18}\)
B. Probability of getting sum as 5 is \(\displaystyle\frac{1}{12}\)
C. Probability of getting sum as 7 is \(\displaystyle\frac{1}{6}\)
D. Probability of getting sum as 6 is \(\displaystyle\frac{1}{9}\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A and C Only
Two dice give \(6\times6=36\) equally likely outcomes, so the probability of a sum = (number of ways to get that sum) ÷ 36. The grid shows the sum for every outcome.
A. Probability of getting sum as 11 is \(\displaystyle\frac{1}{18}\) Correct. Sum 11 comes in 2 ways, (5, 6) and (6, 5), so the probability is \(\displaystyle\frac{2}{36}=\frac{1}{18}\).
B. Probability of getting sum as 5 is \(\displaystyle\frac{1}{12}\) Incorrect. Sum 5 comes in 4 ways, (1, 4), (2, 3), (3, 2), (4, 1), so the probability is \(\displaystyle\frac{4}{36}=\frac{1}{9}\).
C. Probability of getting sum as 7 is \(\displaystyle\frac{1}{6}\) Correct. Sum 7 comes in 6 ways, (1, 6) to (6, 1), so the probability is \(\displaystyle\frac{6}{36}=\frac{1}{6}\).
D. Probability of getting sum as 6 is \(\displaystyle\frac{1}{9}\) Incorrect. Sum 6 comes in 5 ways, (1, 5) to (5, 1), so the probability is \(\displaystyle\frac{5}{36}\).