Multiple choice

Two symmetrical dice are thrown $200$ times. Getting a sum of $9$ points is considered to be a success. The probability distribution of successes is

  1. $\left( 200,\ \cfrac { 1 }{ 9 } ,\ \cfrac { 8 }{ 9 } \right) $
  2. $\left( 200,\ \cfrac { 2 }{ 9 } ,\ \cfrac { 7 }{ 9 } \right) $
  3. $\left( 200,\ \cfrac { 4 }{ 9 } ,\ \cfrac { 5 }{ 9 } \right) $
  4. $\left( 200,\ \cfrac { 1 }{ 4 } ,\ \cfrac { 3 }{ 4 } \right) $
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A Correct answer
Explanation

Sum of 9 with two dice: (3,6), (4,5), (5,4), (6,3) = 4 outcomes out of 36. Probability p = 4/36 = 1/9. q = 1 - p = 8/9. Binomial distribution is (n, p, q) = (200, 1/9, 8/9).

AI explanation

The probability distribution of successes follows a binomial distribution with parameters n, p, and q. The total number of trials is n = 200. A sum of 9 from two dice has 4 favorable outcomes out of 36, making p = 1/9 and q = 1 - 1/9 = 8/9. Therefore, the distribution is (200, 1/9, 8/9).

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