Combinatorics - math word problems - page 48 of 57
Number of problems found: 1135
- Probability
In an election, 2,400,000 voters out of a total of 6,000,000 voted for party Z. Three voters are selected at random. Let the random variable ξ = {number of voters for party Z among the three selected}. Determine: a) the probability distribution, the distr - Three cartridges - shooting
A shooter has three cartridges. He decided that he would shoot at the target until he hits for the first time. The probability of a hit at each shot is 0.6. The random variable X gives the number of cartridges fired. a) Write the probability distribution - Phone call probability
One hundred people work in the office. Each of them spends an average of 25 minutes daily on the phone. A working day has 8 hours. What is the probability that ten workers will be on the phone simultaneously in one day? - Probability of malaria
A survey at a hospital indicates that the probability of a patient testing positive for malaria is 0.6. Two patients are selected at random. What is the probability that: (i) one tests negative and the other tests positive? (ii) both patients test positiv - Pass a test
The student has to pass a test that contains ten 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 randomly chose the answers. What are the probabilities that the student - Sample Proportion
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. Four hundred students are randomly selected from the college, and 224 of - Lifespan
The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours. a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours? b) To what value of L hours can the la - Six segmants
Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options. - Isosceles triangle construction
There are six lines 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm long, two of each length. How many isosceles triangles can be constructed from them? List all options. - An exam - normal distribution
Five thousand students take an exam with a mean of 59 and a deviation of 8. How many students will score less than 75? - Genetic disease
One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has three children. What is the probability of this family having one child who inher - Guests - party
There are 13 guests at a party. They clink their wine glasses with each other. How many clinks will we hear in total? - Each with each
Five pupils from the 3 A class played table tennis. How many matches did they play with each other? - Tournament match calculation
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe? - From experience Based on the experience of an insurance company employee, it was found that an insurance payout under household insurance exceeds 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims: a) at least 5 will ex
- Crime solving probability
The police solved 21 crimes in the monitored period. The probability of solving a crime is 0.64. What is the probability that the police: a) just solved 7 crimes b) did not solve at least 2 criminal offenses P.S. Let's assume ideal police officers - Component deviation probability There are 200 components in the production batch, of which 26 have a plus deviation from the nominal value. Calculate the probability that none of the 10 products selected will have a positive variance if we make selections without repetition
- Component failure probability
The daily product consists of 1000 components, and the probability of failure of any component during the use of the device is 0.001. It does not depend on other components. What is the probability of failure of two components in the investigated period o - Families 2
Seven hundred twenty-nine families have six children each. The probability of a girl is 1/3, and the likelihood of a boy is 2/3. Find the number of families having two girls and four boys. - 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 three decimals).
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