Question

You are a student presenting your thesis to get a doctorate. The panel who will vote to grant you your doctorate (or not) is comprised of 7 professors. Your read of the panel tells you that each professor has a 0.4 chance of voting to deny your doctorate, independently of the others. If the panel reaches a decision by majority rule, what is the probability that the panel will grant you your doctorate? Majority rule, of course, implies that 4, 5, 6 or 7 professors must be in agreement.

Answer 1

Probability of voting to deny the doctorate by a professor = 0.4

The problem can be solved using Binomial distribution with parameters n = 7 and p = 0.4

For a binomial distribution:

The probability of getting doctorate is same as the probability of getting less than 4 votes against thesis i.e.,:

Therefore, the required probability is 0.7101