Exam P Free Sample Questions
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Section 1: General Probability
Preparing for Exam P? Here’s three free sample questions from the general probability section (this section makes up 23-30% of the test), so you can do well on your next exam sitting. These questions cover basic concepts of probability and discrete mathematics.
1. An ordinary die and a die whose faces have 1, 4, 4, 7, 8, 9, dots are tossed independently of one another, and the total number of dots on the two dice is recorded as N. Find the probability that N < 9?
2. A survey of 1000 college students who play video games was taken. Survey respondents indicated if they were either a PUBG fan, a Fort fan or both. 600 indicated they were a fan of PUBG and 900 indicated they were a fan of Fort. Find the probability that a college student is not a fan of PUBG given that they are a fan of Fortnite?
3. An auto insurance company classifies its policies in four categories: platinum, gold, silver, and bronze. Of the company’s policyholders, 10% are platinum, 40% are gold, 35% are silver, and 15% are bronze. Each platinum policyholder has probability of 0.001 of having an accident in the next year, each gold policyholder has probability of 0.005 of having an accident in the next year, each silver policyholder has probability 0.01 of having an accident in the next year, each bronze policyholder has probability 0.05 of having an accident in the next year. A policyholder gets into an accident in the next year. What is the probability that the policyholder was gold?
4. Suppose that customers arrive at a car dealership at a mean rate of 5 per hour. Assuming that the number of arrivals per time period follows a Poisson distribution. Calculate the probability that at least 2 customers arrive in the next hour?
5. The probability that the players on a hockey team will have no injuries in a given week is 75%. Assuming that the number of injuries from week to week are independent, what is the probability that the fifth week in a season is the first week that at least one injury occurs?
6. The battery lifetime of a mobile device has an exponential distribution with a median of ten hours. Calculate the probability that the device will last without failing for at least 11 hours?
Next Section
Section 2: Univariate Random Variables
This section contains discrete univariate distributions (e.g., binomial, geometric, Poisson, and uniform) and continuous univariate distributions (e.g., exponential, lognormal, normal, and uniform). Here are a couple of free sample questions from this section. This section makes up 44-50% of the test.
Final Section
Section 3: Multivariate Random Variables
This part of the exam contains questions on discrete and continuous settings related to multivariate distributions, the distribution of order statistics for independent random variables, and linear combinations. This is the final section and makes up 23-30% of the exam.