Question

A contest consists of predicting the results win, draw or defeat of 7 football matches. A sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is

• A. $\frac { 8 } { 3 ^ { 7 } }$
• B. $\frac { 16 } { 3 ^ { 7 } }$
• C. $\frac { 280 } { 3 ^ { 7 } }$
• D. $\frac { 560 } { 3 ^ { 7 } }$

Answer 1

Answer: (C)

$\frac { 280 } { 3 ^ { 7 } }$

Answer 2

$P$ (correct prediction) $= \frac { 1 } { 3 }$ ; $P$ (wrong prediction) $= \frac { 2 } { 3 }$

For exactly 4 right predictions

Probability $= { } ^ { 7 } C _ { 4 } \left( \frac { 1 } { 3 } \right) ^ { 4 } \cdot \left( \frac { 2 } { 3 } \right) ^ { 3 } = \frac { 280 } { 3 ^ { 7 } }$