Combinatorics - math word problems - page 55 of 57
Number of problems found: 1135
- The university
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in the - Prisoners
It is estimated that 10% of all federal prisoners have a positive self-image, 40% have a neutral self-image, and the rest have a negative self-image. The estimated probability of rehabilitating a prisoner with a negative self-image is 0.1. With a neutral - Flu probability
In the monitored group of people, 8% are ill with the flu. One hundred people from this group were examined. What is the probability that at most 5 of them will be sick with the flu? (round to 3 decimal places) - Z6 – I – 6 MO 2019
A mother was studying multi-digit numbers in which odd and even digits alternate regularly. She called those starting with an odd digit 'comical' and those starting with an even digit 'cheerful'. (For example, the number 32387 is comical, and the number 4 - TV fail
On average, a television set experiences 25 failures per 10,000 hours of use. Find the probability of a failure occurring within 400 hours of operation. - Biathlete shooting probability
According to long-term statistics, a biathlete has a shooting success rate of 72%. a) what is the probability that 4 targets will be hit on one item (5 shots). b) what is the probability that fewer than 4 targets are hit on one item (5 shots)? - Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high-temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because precisely one of t - Side effect probability
The probability of an adverse drug reaction is 2.1%. How many people need to be prescribed for one patient to experience side effects with a chance of 90%? - Shooter hit probability In the shooting competition, each shooter fires 5 shots. Shooter Muška will hit the target with one shot with a probability of 60%. What is the probability that he hits at least once out of five shots?
- Spindle distribution
The worker operates 600 spindles on which the yarn is wound. The probability of tearing the yarn on each spindle at time t is 0.005. a) Determine the probability distribution of the number of torn spindles at time t and the mean and variance. b) What is t - Doctors
The drug successfully treats 90% of cases. Calculate the probability that it will cure at least 18 patients out of 20. - Counting hairs
Find out if two people in Bratislava have the same number of hairs on their heads. Instructions. Bratislava has about 420,000 inhabitants, and a person has less than 300,000 hairs on his head. - Probability - defective parts
There are 10 parts in the box, and 3 of them are defective. Let's choose 4 components at random. What is the probability that it will be among them a) 0 defective, b) just one defective component, c) just two defective components, d) exactly 4 defective c - Error rate
The exam has six questions. Students have an error rate of 20% and can have a maximum of 1 question wrong. What is the probability that they will succeed? - Bernoulli trial
A used car saleswoman estimates that each time she shows a customer a car, there is a probability of 0.1 that the customer will buy the car. The saleswoman would like to sell at least one car per week. If showing a car is a Bernoulli trial with a probabil - Position of digits
Find a number with six digits. If you put the last digit before the first, you get a new number that is five times larger. The digits between must not change their position. - Drinks In a country, 65% of people drink coffee, 50% drink tea, and 25% drink both. What is the probability that a person chosen at random will drink neither tea nor coffee?
- We are planting
We are planting 2 types of roses (white and red). Experience shows that the probability of a red rose taking root is 0.7. A total of 5 seedlings are planted. What is the probability that: a) the first 2 will be red and the next 3 white? b) all will be red - Tile defect probability
The factory produces 35% of the tiles on line A, which produces scrap with a probability of 0.02, and 65% on line B, where the probability of scrap is 0.03. What is the probability that the selected tile will be defective? - Balls
We have n identical balls (numbered 1-n) selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides wi
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