Whats the chance of getting 25/40 multiple choice questions right.
1 Answer
The odds of answering exactly 25 questions correectly is
\[{40 \choose 25}(\frac{1}{4})^{25}(\frac{3}{4})^{15}=0.00000047744016\approx 0\%\]
You will pass if you answer at least $25$ questions correcxtly. So the probability is
\[{40 \choose 25}(\frac{1}{4})^{25}(\frac{3}{4})^{15}+{40 \choose 26}(\frac{1}{4})^{26}(\frac{3}{4})^{14}+\dots +{40 \choose 40}(\frac{1}{4})^{40}(\frac{3}{4})^0\]
\[=\sum_{n=25}^{40}{40 \choose 25}(\frac{1}{4})^{n}(\frac{3}{4})^{40-n}=0.00000058796594= 0\%.\]
Indeed ${40 \choose 25}(\frac{1}{4})^{n}(\frac{3}{4})^{40-n}$ is the probability that you answer exactly $n$ questions correctly. In order to pass $n$ could be any number between $25$ and $40$ and that is why we are adding the probabilities. You can use this website to calculate probabilities:
https://www.gigacalculator.com/calculators/binomial-probability-calculator.php

- 1 Answer
- 143 views
- Pro Bono
Related Questions
- What is the probability that the last person to board an airplane gets to sit in their assigned seat?
- Trajectory detection in noise - the probability of at least one random point being within epsilon distance of the trajectory?
- How do you calculate per 1,000? And how do you compensate for additional variables?
- Joint PDF evaluated over a curve $P_{U,V}$
- Correlation of Normal Random Variables
- How to calculate how much profit a loan of a certain risk level (based on dice rolls) is likely to make?
- Probability maximum value of samples from different distributions
- Questions for Statistics Project