# Reason + percentages - math problems

#### Number of problems found: 86

- Error rate

The exam has 6 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? - The vaccination

The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated more likely to be infected? Consider N = 10,000 inhabitants and K = 1,000 infected. b. How many times more likely are unvaccinate - 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 - Fresh juice

The seller offers fresh-squeezed juice, which the customer either pours into his own containers or sells in liter plastic bottles, which the customer buys from him. A liter of juice costs 40 CZK more than a bottle. There is no charge for turning the juice - Beer tapping

When checking compliance with the beer tapping, it was found that 60% of the offered beers were underfilled. The others were fine. Thus, instead of 0.5 l, the volume was 4.4 dcl on average. What was the volume of one average underfilled beer? - Birthday paradox

How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%? - The manufacturer

The manufacturer found that 3% of the plates produced had a malfunction. Of the compliant, 75% are first and 25% second. What is the probability of producing first and second class plates? - Probability

How probable is a randomly selected three-digit number divisible by five or seven? - The test

The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer - 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%? - Bdf tablet

Detective Harry Thomson has come across a surprising mystery. As part of the weekend's action, the tablet he looked for dropped by 30%. He also recommended this bargain to his friend. However, it came to the shop on Monday, and the tablet was 30% more exp - Students

If the fifth-grade class left 20% of students and in the seventh grade were added two pupils, in the eighth one pupil, the number has not changed in the ninth grade, but it is now tenth students less than it was in the fifth grade. How many pupils are in - Harvest time

Grandma and granddaughter Julka reap currants in 15 hours of working together. Julka herself would have currants 10 days after 6 hours of work a day. Find by what percentage the grandma's harvest time was shortened when the granddaughter was involved in c - Before yesterday

He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the - Cut trees

There are 1,200 trees in the grove, of which 55 percent are deciduous, the remaining coniferous. Workers cut down 35 percent a) trees, b) deciduous trees, c) coniferous trees. How many trees now have this grove? - Folding table

The folding kitchen table has a rectangular shape with an area of 168dm^{2}(side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu - Geography tests

On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests? - Prospering students

There are girls and 30 boys in the class. Boys prospering 28, girls all. How many girls are in the class and how many boys are there, if all the prospering students are 95%? - Lemonade

In January, 2 liters of lemonade were sold for CZK 24, while in February, 2.5 liters of lemonade sold at same price. How much percent was 1 liter of lemonade cheaper in February than in January? - Math test

Obelix filled a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points, for each bad answer he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctly?

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