# An exam has two parts. Raul has probability .9 of answering a question from part A correctly and .7 of answering a question from part B correctly. What is the probability that Raul's grade is greater than 75%?

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Part A contains 25 questions and part B contains 36 questions. Assume that answering each question correctly are independent events.

Part A contains 25 questions and part B contains 36 questions. Assume that answering each question correctly are independent events.

##### 1 Answer

I got roughly 76.3%

#### Explanation:

Let's first of all see that we have binomial probabilities with answering Part A and Part B of the exam. The general form of a binomial probability is:

For Part A it's

and for Part B:

When we sum up the summations, we end up with 1 for both Part A and Part B - in essence, the entirety of the probability results.

What we're looking for are combinations of results where Raul ends up with greater than a 75% mark. Each question appears to be worth the same, and so he needs to get:

and so he needs to get 46 or more right to achieve the needed score. And so we will multiply results from Part A and Part B that will get us to 46 or more answers right.

This means that if Raul gets all of Part A right (25 questions), he can get at least 21 Part B questions right and be ok:

for a total of 136 multiplications. Which I'll do on a separate spreadsheet.

I got roughly 76.3%