Multiple choice

A symmetrical die is tossed twice. Getting a four is considered to be a success. The mean and variance of number of successes are

  1. $\cfrac { 2 }{ 3 } ,\ \cfrac { 5 }{ 18 } $
  2. $\cfrac { 1 }{ 3 } ,\ \cfrac { 5 }{ 18 } $
  3. $\cfrac { 1 }{ 3 } ,\ \cfrac { 7 }{ 18 } $
  4. $\cfrac { 2 }{ 3 } ,\ \cfrac { 7 }{ 18 } $
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B Correct answer
Explanation

This is a binomial distribution with n=2 and p=1/6 (probability of getting a 4). Mean = np = 2 * (1/6) = 1/3. Variance = npq = 2 * (1/6) * (5/6) = 10/36 = 5/18.

AI explanation

This is a binomial distribution where the number of trials is 2 and the probability of success on a single die is 1 divided by 6. The mean is calculated as n multiplied by p, giving 2 times 1/6 to equal 1/3. The variance is calculated as n multiplied by p multiplied by (1 minus p), which is 2 times 1/6 times 5/6 to equal 10/36 or 5/18. The mean and variance are 1/3 and 5/18 respectively.

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