Question

A contest consists of predicting the results win, draw or defeat of 7 foot ball 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

The correct option is C $\frac{280}{3^7}$

Since no additional information is given, we have to assume that the probability of each of the results is same and is equal to $\frac{1}{3}$.
Now using binomial probability, we have to find the probability of 4 success in 7 trials. Probability of r successes in n trials is equal to ${}^n{C}_r{p}^r{q}^{n-r}$, where p is the probability of success in one trial and q is the probability of failure in one trial.
Probability = ${}^7{C}_4{\left(\frac{1}{3}\right)}^4{\left(\frac{2}{3}\right)}^3=\frac{280}{3^7}$.