Multiple choice

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than $5$ is ______

  1. $\dfrac {5}{36}$
  2. $\dfrac {1}{6}$
  3. $\dfrac {5}{18}$
  4. $\dfrac {13}{18}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum > 5: Total outcomes = 36. Sum <= 5: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1) = 10 outcomes. Sum > 5 = 36 - 10 = 26 outcomes. 26/36 = 13/18.

AI explanation

When two dice are thrown, the total number of possible outcomes is 36, and the complementary event to getting a sum more than 5 is getting a sum of 5 or less. The outcomes that result in a sum of 2, 3, 4, or 5 are 10 specific combinations: (1,1), (1,2), (2,1), (1,3), (3,1), (2,2), (1,4), (4,1), (2,3), and (3,2). The probability of this complementary event is 10/36, so subtracting it from 1 yields 1 - 10/36 = 26/36, which simplifies to 13/18. The probability is 13/18.

Keep practicing — related questions