Question

The probability that a student is not a swimmer is 1/5. What is the probability that out of 5 students, 4 are swimmers

• A. ${ } ^ { 5 } C _ { 4 } \left( \frac { 4 } { 5 } \right) ^ { 4 } \frac { 1 } { 5 }$
• B. $\left( \frac { 4 } { 5 } \right) ^ { 4 } \frac { 1 } { 5 }$
• C. ${ } ^ { 5 } C _ { 1 } \frac { 1 } { 5 } \left( \frac { 4 } { 5 } \right) ^ { 4 } \times { } ^ { 5 } C _ { 4 }$
• D. None of these

Answer 1

Answer: (A)

${ } ^ { 5 } C _ { 4 } \left( \frac { 4 } { 5 } \right) ^ { 4 } \frac { 1 } { 5 }$

Answer 2

The probability that student is not swimmer

$p = \frac { 1 } { 5 }$ and probability that student is swimmer $q = \frac { 4 } { 5 }$.

$\therefore$ Probability that out of 5 students 4 are swimmer

$= { } ^ { 5 } C _ { 4 } \left( \frac { 4 } { 5 } \right) ^ { 4 } \left( \frac { 1 } { 5 } \right) ^ { 5 - 4 } = { } ^ { 5 } C _ { 4 } \left( \frac { 4 } { 5 } \right) ^ { 4 } \left( \frac { 1 } { 5 } \right)$