Multiple choice

A pair of dice are thrown, if 5 appears on atleast one of the dice, then the probability that the sum is 10 or greater, is

  1. $\dfrac { 11 }{ 36 } $
  2. $\dfrac { 2 }{ 9 } $
  3. $\dfrac { 3 }{ 11 } $
  4. $\dfrac { 1 }{ 12 } $
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C Correct answer
Explanation

Sample space where 5 appears on at least one die: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (1,5), (2,5), (3,5), (4,5), (6,5). Total = 11 outcomes. Sum >= 10: (5,5), (5,6), (6,5). Total = 3 outcomes. Probability = 3/11.

AI explanation

When two dice are thrown, the condition that at least one die shows a 5 yields 11 possible outcomes: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (1,5), (2,5), (3,5), (4,5), (6,5). The favorable outcomes where the sum is 10 or greater are (5,5), (5,6), and (6,5), making 3 favorable outcomes. Using the conditional probability formula, the probability is the ratio of favorable outcomes to the restricted sample space, which is 3/11.

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