Question

A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are

• A. $\frac { 1 } { 2 } , \frac { 1 } { 12 }$
• B. $\frac { 1 } { 6 } , \frac { 5 } { 12 }$
• C. $\frac { 5 } { 6 } , \frac { 1 } { 2 }$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

We are given that $n = 3$ $p = \frac { 1 } { 6 }$ $q = \frac { 5 } { 6 }$

Mean $= n p = 3 \times \frac { 1 } { 6 } = \frac { 1 } { 2 }$

Variance $= n q p = 3 \times \frac { 1 } { 6 } \times \frac { 5 } { 6 } = \frac { 5 } { 12 }$