Probability Problem

Quick help

So I've been trying to know the probability of a student, who have never studied anything, getting a score higher than $75\%$ of the total items of the test.

Here's the situation:

Jason is taking a $50$ -item ABCD-multiple-choice test about a topic he doesn't know and never reviewed about. Unbiased, he answered them randomly. What is the probability that Jason gets a score higher than $37$ ?

I'm confused on when to use addition and multiplication on probability problems.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

He could get 38 right, or 39 right, or 40 right, etc. And there are many ways to get 38 right, for example. So think the answer is:

Ptotal = (50 choose 38)*(Pright^38)(P_wrong^12) + (50 choose 39)(Pright^39)*(Pwrong^11) + ...........etc, etc.

Steven Chase - 2 years, 3 months ago

So what would be the result? Can I ask for a step-by-step solution for this one?

Kaizen Cyrus - 2 years, 3 months ago

How many possibilities are there for each multiple choice problem?

Steven Chase - 2 years, 3 months ago

@Steven Chase – A-B-C-D are the choices, so $4$ .

Kaizen Cyrus - 2 years, 3 months ago

@Kaizen Cyrus – Let's say N is the number of problems the student gets right. N can be anything from 0 to 50. If you calculate the probability for each N (as I explained above), and sum all probabilities up from 0 to N, you get 1, as expected. The probability of getting 38 or more right is basically zero. The combined probability for N >= 25 is about 0.00012. The combined probability for N >= 12 is about 0.6184. My spreadsheet contains 51 rows, but only 7 are displayed here.

Steven Chase - 2 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$