Sets + percentages - practice problems
Number of problems found: 32
- A disease
A disease affects 10% of the individuals in a population, and a sample of 100 people was selected from the population. What is the probability of finding the disease in at least 15 people? - False positive, false negative
Suppose the likelihood of someone being allergic to cats is 1/1000 of the general population. A test to determine if you're allergic to cats has a false positive rate of 5%; that is, 5% of the time, the test will indicate incorrectly that you are allergic - A math
A math teacher teaches Geometry and Precalculus. 37% of students take both math classes, and only 39% take just Geometry. What is the probability that a student will attend Precalculus given that they attended Geometry? What is the percentage of students - 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 - Students and exam
In a certain college, accounting is one of the courses; among the accounting students, 60% are male. Among the male students, 75% passed the exams, while among the females, 50% failed. (a) present this using a probability tree diagram (b) determine the pr - Social beneficiaries
In a certain community, 52% are SAP beneficiaries, 15% are members of 4Ps, and 8% are both SAP and 4 Ps. If a citizen from the community is an SAP, what is the probability that he also is 4Ps? If that person is not a 4Ps, what is the probability that he i - Cancer in woman population
In a particular population of women, 40% have had breast cancer, 20% are smokers, and 13% are smokers and have had breast cancer. If a woman is selected at random from the population, what is the probability that she has breast cancer, smokes, or both? - Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm - Drinks
In a country, 65% of people drink coffee, 50% drink tea 25% drink both. What is the probability that a person chosen at random will drink neither tea nor coffee? - Unidentified 61201
The set contains 12 different figures. How many unidentified individual figures do I have to buy to have precisely two complete sets with a 90% probability after unpacking them? - Three robots
In a workshop, three robots, Q, R, and S, are employed to make chairs Robot Q makes 25% of the chairs Robot R makes 45% of the chairs The remaining chairs are made by Robot S Evidence has shown that 2 percent of the chairs made by robot Q are - The vaccination
The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated and more likely to be infected? Consider N = 10,000 inhabitants and K = 1,000 infected. b. How many times more likely are unvacci - An aircraft
An aircraft manufacturing company has submitted bids on two separate airline contracts, A and B. The company feels it has a 70% chance of winning contract A and a 25% chance of winning contract B. Furthermore, it believes that winning contract A is indepe - 25 pupils
Twenty-five pupils attend the school dance group, which is 5 percent of all pupils. The judo class is attended by 20 pupils, a quarter of whom also go to a dance group. How many schoolchildren do not go to a dance or judo group? - Gym center
80% of all visitors to the gym center enjoy a discount. 3/4 of all visitors go to practice regularly. All visitors who go to the gym regularly benefit from a discount. What percentage of all visitors do not go to the gym regularly but still use the discou - Hazard game
In the Sportka hazard game, six numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess five numbers correctly) b) the third prize (we guess four numbers correctly)? - Defective 23221
The factory sets a standard that 2% of products may be defective. Last week, out of 1,250 products, 32 were defective. How many defective products were the standard exceeded? - Alarm systems
What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%? - 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 - N percentille problem
Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
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