Question

A biology quiz consists of 14 multiple-choice questions. Nine must be answered correctly to receive a passing grade. If each question has 4 possible answers,what is the probability that a student who guesses at random will pass?

Answer 1

0.0022

Explanation:

Answer 2

`0.002154`

Explanation:

`C(14,9) (1/4)^9 (3/4)^5 + C(14,10) (1/4)^10 (3/4)^4 + C(14,11) (1/4)^11 (3/4)^3 + C(14,12) (1/4)^12 (3/4)^2 + C(14,13) (1/4)^13 (3/4) + (1/4)^14 = 0.001812 + 0.000302 + 0.000037 + 0.000003 + 0.000000 + 0.000000 = 0.002154`

`C(n,k) = (n!) / ((n-k)!k!)`

Answer 3

`0.0022`

Explanation:

This is Binomial with `n= 14, p= 1/4 = 0.25` and you need to find this probability:

`P(X >= 9)` = Sum from `x=9` to `x = 14: 14Cx (0.25^x)(0.75)^(14-x)`

If you some all 6 terms of this Binomial you will get the answer:

`P(X >= 9) = 0.0022`