Multiple choice

When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8.

  1. $\dfrac{1}{5}$
  2. $\dfrac{2}{5}$
  3. $\dfrac{3}{5}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum = 8 outcomes: (2,6), (3,5), (4,4), (5,3), (6,2). Total = 5. Favorable (first > second): (5,3), (6,2). Total = 2. Probability = 2/5.

AI explanation

Using the conditional probability formula, we find the favorable outcomes where the sum is 8, which are (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2), giving 5 total outcomes. Out of these, the outcomes where the first die has a greater number than the second are (5, 3) and (6, 2), providing 2 favorable outcomes. The required probability is therefore 2/5.

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