# A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. If a student guesses on every question, what is the probability of getting exactly 9 correct?

Jul 27, 2017

P(9)=.1298

#### Explanation:

This is an example of when to use the binomial distribution. The binomial distribution is when you are given a set number of trials, and are asked what is the probability of getting a certain number or range of successes. In this case the number of trials is 30 (there are 30 questions) and the number of successes we are looking for is 9 right. We then would use this formula

P(X)= $n C r {\left(p\right)}^{r} {\left(q\right)}^{n - r}$

1. n is the number of trials
2. r is the number of successes
3. p is the probability of success
4. q is the probability of failure

This is the binomial formula (may have seen it before). It is very useful in the field of statistics.
Imputing the information given, we get the formula

$30 C 9 {\left(.25\right)}^{9} {\left(.75\right)}^{21}$= .1298