Combinatorial number + probability - practice problems
Number of problems found: 53
- Pass a test
The student has to pass a test that contains 10 questions. For each of them, he chooses one of 5 answers, with just one being correct. The student did not prepare for the test, so he chooses the answers at random. What are the probabilities that the stude
- Population variance
In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. If 8 students are randomly selected, find the population variance σ² of
- Binomial probability
What is the binominal probability that at least 4 of the 6 trials (n=6) are succeeded where φ = 0.50?
- Draw a triangle
We have line segments with lengths of 3cm, 5cm, 6cm, 7cm and 9cm. What is the probability in % that if I randomly select three of them I will be able to draw a triangle?
- Created trio
What is the probability that in the created trio, which consists of 19 boys and 12 girls, they will be: a) the boys themselves b) the girls themselves c) 2 boys and 1 girl?
- Bernoulli distribution
The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).
Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate?
- Wimbledon finals
Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus. If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
- A license
A license plate has 3 letters followed by 4 numbers. Repeats are not allowed for the letters, but they are for the numbers. If they are issued at random, what is the probability that the 3 letters are in alphabetical order and the 3 numbers are consecutiv
Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most two men suffer from alopecia.
- Playing cards
From 32 playing cards containing 8 red cards, we choose 4 cards. What is the probability that just 2 will be red?
During the hygienic inspection in 2000 mass caterers, deficiencies were found in 300 establishments. What is the probability that deficiencies in a maximum of 3 devices will be found during the inspection of 10 devices?
- Hazard game
In the Sportka hazard game, 6 numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess 5 numbers correctly) b) the third prize (we guess 4 numbers correctly)?
- Six questions test
There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
- Probability of failures
In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than one failure among the 100 selected products if we return the selected products to the file after the check.
- All use computer
It is reported that 72% of working women use computers at work. Choose 3 women at random, find the probability that all 3 women use a computer in their jobs.
- Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chair between them if people choose their place completely at random?
- Sick days
In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. .. what is the probability an employee will use 17 OR MORE sick days in a year?
See also our combinations calculator. Combinatorial number - practice problems. Probability - practice problems.