Multiple choice

If a die is rolled twice, find the probability of getting an even number in the first time or a total of $8$.

  1. $\dfrac{5}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{7}{9}$

  4. none
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A Correct answer
Explanation

P(Even first) = 3/6 = 1/2. P(Total 8) = P((2,6), (3,5), (4,4), (5,3), (6,2)) = 5/36. P(Even first AND Total 8) = P((2,6), (4,4), (6,2)) = 3/36 = 1/12. P(A or B) = P(A) + P(B) - P(A and B) = 1/2 + 5/36 - 1/12 = 18/36 + 5/36 - 3/36 = 20/36 = 5/9.

AI explanation

Using the addition theorem of probability, P(A or B) = P(A) + P(B) - P(A and B), where event A is getting an even number on the first roll and event B is getting a sum of 8. P(A) is 18/36, P(B) is 5/36, and P(A and B), which means an even first number and a sum of 8, has outcomes (2, 6), (4, 4) and (6, 2), so P(A and B) is 3/36. The probability is 18/36 + 5/36 - 3/36 = 20/36 = 5/9.

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