# Intersection of sets - math problems

#### Number of problems found: 69

- 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? - An aircraft

An aircraft manufacturing company has submitted bids on two separate airline contracts, A and B. The company feels that 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 i - And-or probabilities

P(A ) = 0.53, P(B) = 0.15, and P(A n B ) = 0.18. Find P(A U B ). Round approximations to two decimal places. - There 11

There are 50 pupil in the class. Out of of this number,1/10 speak French only and 4/5 of the 10 remainder speak both French and English . If the rest speak English only find the number of students who speak only English? - Smoker male

For a person selected randomly from a certain population, events A and B are defined as follows. A = event the person is male B = event the person is a smoker. For this particular population, it is found that P(A ) = 0.53, P(B) = 0.15, and P(A n B ) = 0.1 - Three subjects

In a class of 40 students, 18 passed mathematics, 19 passed accounts, 16 passed economics, 5 mathematics and accounts only, 6 mathematics only, 9 accounts only, 2 accounts and economics only, if each student offered at least one of the subjects. a) how ma - A swimmer-training

A swimmer-training program has 26 students specializing in the butterfly stroke, 24 specializing in the breaststroke, and 29 specializing in the backstroke. Of these students, 5 students are specializing in all three strokes, 5 are specializing in only th - 25 pupils

25 pupils attend the school dance group, which is 5 percent of all pupils in the school. The judo class is attended by 20 pupils of the school, 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 - In a 5

In a football game, Mike, gets to play be the goalkeeper 50% of the time if Peter is the coach. But if Robert is coaching, he only has 30% chance. Peter coaches more than Robert in about 6 to 10 games. What is the probability that Mike gets to be the goal - Group of children

There is a group of children. There is a boy named Adam in each of the three children subgroup and a girl named Beata in each quartet (four-member subgroup). How many children can be in such a group and what are their names in that case? - Open intervals

Open intervals A = (x-2; 2x-1) and B = (3x-4; 4) are given. Find the largest real number for which A ⊂ B applies. - Operations with sets

The set B - A has twice as fewer elements than the set A - B and four times fewer elements than the set A ∩ B. How many times more elements does the set A have than the set B? - MF graduate

78 school students graduate from mathematics or physics. There are three times more students who graduate from mathematics and do not graduate from physics than those who graduate from physics and do not graduate from mathematics. 69 students graduate fro - Subtracting sets

For two sets K, L is true: K has 30 elements, L has 27 elements and the set L - K has 22 elements. How many elements does the set K - L have? - Venn diagram

University students chose a foreign language for the 1st year. Of the 120 enrolled students, 75 chose English, 65 German, and 40 both English and German. Using the Venn diagram, determine: - how many of the enrolled students chose English only - how many - Language courses

Of the company's 60 employees, 28 attend an English course, 17 take a German course, and 20 do not attend any of these courses. How many employees attend both courses? - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Coordinates of the intersection of the diagonals

In the rectangular coordinate system, a rectangle ABCD is drawn. The vertices of the rectangle are determined by these coordinates A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele

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