Question

How many ways are there to correctly answer 2 out of 7 true or false questions

Answer 1

First thought is that each question has 2 possible answers, so might need to consider multiplication rule as well.

Answer 2

This is a binomial setting, I think.

Answer 3

Oh, fail :)
not as easy as I thought it was. lol

Answer 4

7 trials, 2 possible outcomes each with fixed random probability.

Answer 5

the 7-choose-2 formula will be used as the binomial coefficient.

Answer 6

The setting asks for 2 successes and 5 failures, but both have the same random probability, so (.5)^2*(.5)^5 is simply (.5)^7 - the same as the probability of any ratio of correct:incorrect out of 7. This is where you multiply by 7C2 to find the number of ways.

Answer 7

This is, of course, assuming that the questions are answered purely randomly (via flip or coin or similar), and the test-taker is not actually trying to answer any correctly - that would change the probabilities of each individual trial and you'd have to use a multi-nomial formula (and likely also Bayes' Theorem to compute those probabilities in the first place).
Simplifying assumptions are good things!

Answer 8

Do you need the formula for the binomial coefficient?