# Math Help - Combinations

1. ## Combinations

A student is writing a test with 4 true/false questions. The student wants to know the theoretical probability of passing the test by guessing. This means that 2 or more of the 4 questions are answered correctly by guessing. Determine this probability and show all your work.

my work:

.5 ^ 2

+

.5^3

+
.5^4

2. Hello,

This is a binomial probability question;
eg. the probability of getting exactly 2 correct is
$4C2\cdot (0.5)^2 \cdot (0.5)^2=0.375$
pr of exactly 3 correct;
$4C3\cdot (0.5)^3 \cdot (0.5)^1=0.25$
and probaility of exactly 4;
$4C4 \cdot (0.5)^4 \cdot (0.5)^0=0.0625$

So the probability of passing $\Pr(X\geq 2)$where $X$ is getting a correct answer is the sum of exactly 2, 3 and 4
hope that helps...

edit, oh... :P