Question

Varun throw two unbiased dice together and gets a sum of 7. If his friend Tarun then throws the same two dice, what is the probability that the sum is less than 7?

• A. $\frac{1}{6}$
• B. $\frac{7}{12}$
• C. $\frac{1}{2}$
• D. $\frac{5}{12}$

Answer 1

Answer: (D)

$\frac{5}{12}$

Answer 2

The number of possibilities where the sum is less than '7' is,
(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)
There are 15 possibilities out of 36(6 x 6) possible outcomes.
∴ The probability that the sum is less than 7 is,
⇒ $\frac{15}{36}=\frac{5}{12}$
Hence, option D is the correct answer.The correct option is (D): $\frac{5}{12}$