Exercise Problems for Discrete Probability Distributions
1. For a multiple choice test, each question has four possible answers of which exactly one is correct. For a test consisting of five questions and a student selects answers at random for all five questions, what is probability that this student will pass that test with at least answered three questions correctly?
2. There are 8 people in a committee, 3 females and 5 males. If a subcommittee is to be formed by selecting 3 members from this committee of 8 people, what is the probability that all of them are female members?
3. A manufacture of computer chip knows that 2% of its chips are defective. A sample of computer chips is to be taken and assuming that each time a chip is selected the chance of that chip to be defective is 2%. So selecting a random sample of 6 chips from all chips manufactured from this company can be considered as a binomial experiment. If a random sample of 6 chips is selected, what is the probability that none of them are defective?
4. It is known that 40% of the cars do not fully stop at a stop sign. If you start to observe cars passing a stop sign, what is the probability that the 10th car that you see is the first car that does not fully stop at the stop sign?
5. It is known that 40% of the cars do not fully stop at a stop sign. If you start to observe cars passing a stop sign, what is the probability that you will see no cars do not fully stop at the stop sign for the first 10 cars?
6. It is known that 4% of the cars passing by your building are made by BMW at any time period. If you start to observe cars from a given time point, what is the probability that 10th car you see is the 3rd BMW?
7. Customers arrive at a travel agency at a mean rate of 3 per 20 minutes from 10:00 a.m. to 2:00 p.m. Assuming that the customers' arrivals follow a Poisson process. Find the probability that no customers will arrive between 12:50 to 1:00 (so that you can sneak out for a quick lunch).
8. To determine how long should a red light hold, the city traffic control engineers observed the traffic and found that on average there are 6 cars arrived at a traffic light per minute from north traveling to south between 1 to 2 p.m. in weekdays. The traffic will be jammed if there are more than 3 cars are waiting in front the traffic light. In a given weekday between 1 to 2 p.m., what is the probability of having a traffic jam if the red light that controlling traffic moving from north to south last for 30 seconds? (That is, what is the probability the there are more than 3 cars arrive at the traffic light in a period of 30 seconds?)
9. A manufacture of computer chip knows that 2% of its chips are defective. A sample of computer chips is to be taken and assuming that each time a chip is selected the chance of that chip to be defective is 2%. So selecting a random sample of 120 chips from all chips manufactured from this company can be considered as a binomial experiment. If a random sample of 120 chips is selected, what is the probability that there are two or less defective chips? (Use Poisson approximation.)