Question

If a test consists of 30 multiple choice questions which all have 5 possible choices each, by random guessing of the answers, what is the possibility of getting 50% on the test.

Answer 1

Do you know the Binomial Distribution?

Answer 2

No.

Answer 3

What are you learning in this chapter/unit?

Answer 4

There are a few different ways to solve this

Answer 5

Basically, the probability of getting 15 right and 15 wrong is (1/5)^15 * (4/5)^15. Then multiply that by (30 choose 15) to allow for the fact that you can get any 15 of them right and still get 50% on the test.

Answer 6

I get 0.00017

Answer 7

that's what I get too (well, 0.000178838, which rounds to 0.00018)

Answer 8

so a 0.02% chance of getting 50% just by guessing?

Answer 9

Of getting exactly 50%, yes. (i.e. not more and not less)

Answer 10

I don't think that's right. When I adjust the number to 12 questions to get 40%, it gives me an even lower probability. Needing to get less right should result in an increase in the chances of getting 40%, no?

Answer 11

I get a higher probability for 12 questions right. can you show me the formula you used?

Answer 12

Okay nvm it worked. But when I do it for 9 questions correct for 31%, I get a 98% chance. That sounds waaay too much.