Percentages + sets - 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
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