Finite Math Probabitlity

Question

In a 20 item true-false examination, if 12 correct answers constitute a passing grade, what are the odds in favor of passing, if he or she is guessing?

Answer 1

This presumably is a binomial density question.

The probability of 12 or more correct answers out of 20 is the sum from k = 12 to 20 of

$\left(\genfrac{}{}{0ex}{}{20}{k}\right)(1/2{)}^{20}$ .

Take this probability as P and Q = 1-P; then the odds ratio is P:Q