Multiple choice

A die is thrown twice. When the sum of their digits be 6 then the probability that atleast one of them will show 4, is

  1. $\frac{1}{6}$
  2. $\frac{2}{5}$
  3. $\frac{3}{5}$
  4. $\frac{1}{2}$
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B Correct answer
Explanation

Given that the sum is 6, the possible ordered outcomes are (1,5), (2,4), (3,3), (4,2), and (5,1), five outcomes in total. Two include at least one 4, so the conditional probability is 2/5.

AI explanation

When two dice are thrown, the condition that the sum of the numbers is 6 restricts our possible outcomes to the sample space of (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). The conditional probability formula requires dividing the number of favorable outcomes by the total outcomes in this restricted sample space. Since there are 2 outcomes that feature at least one 4 out of 5 total possible outcomes, the probability is 2/5.

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