# I need help what formula would i use or what steps do i take?

A professor gives a test with 100 true-false questions. If 60 or more correct is necessary to pass, what is the probability that a student will pass by random guessing?

The brute force way of doing this is add up the probabilities of getting 60, 61, 62.. and up to 100 correct. The number will get very small when you get past 70, so you can forget about their contribution. The probability of getting 60 is
(1/2)^100* [100!/(60!*40!)] = 0.01084
You can also do it by computing the standard deviation of the distribution and using the error function integral from 60 to infinity

is there a website for this type of equation.

## Yes, there are online calculators and websites that can help you with probability calculations like this one. One popular website is Wolfram Alpha (www.wolframalpha.com).

To use Wolfram Alpha, you can simply enter the equation or problem statement, such as "probability of passing with random guessing on a 100-question true-false test," and it will provide you with the answer and potentially even show you the step-by-step solution.

Alternatively, you can search for online probability calculators that specifically deal with binomial probability, as this problem involves a binomial distribution. These calculators will usually ask you to input the number of trials, the probability of success, and the desired outcome (in this case, passing with at least 60 correct answers) to determine the probability.