Intersection of sets - practice problems - page 3 of 11
Number of problems found: 212
- Triangle height intersection
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Dice even probability
We roll the dice three times. Calculate the probability of getting an even number on the first, second, or third toss. - 200 students
200 students sat exams in Czech, mathematics, and physics. 114 students passed Czech, 50 passed mathematics, and 41 passed physics. 14 students passed both Czech and mathematics, 15 passed both mathematics and physics, and 11 passed both Czech and physics - Favourite singers A poll carried out among 200 students of one school found out which of the singers V. Neckář, K. Gott, W. Matuška is the most popular. It brought the following results: Gott is popular with 78 students, Matuška with 75 students, and Neckář with 101. It wa
- Collection of medicinal plants
A pensioners' club organised a collection of medicinal plants. Two pensioners could not participate in the collection for health reasons, the others decided to collect dead-nettle, elder, and coltsfoot. All three herbs were collected by 7 pensioners, dead - Fish mushroom respondents
Out of 32 people, 22 like fish. Four fewer people will enjoy the mushrooms. Those who eat mushrooms or fish are 7 times more than those who do not eat mushrooms or fish. How many of the respondents have fish and mushrooms? - In the fifth In the fifth grade, which is attended by 88 pupils, two elective subjects are taught: mathematics exercises and sports games. 66 pupils did not attend mathematics exercises, which is 3 more than the number of pupils who did not sign up for sports games. 9
- Dice coin probability
We roll the dice and then toss the coin as many times as the number that came up on the dice. What is the probability that the coin lands head at least once? - Written test
A written test was taken by 35 students, the test contained 3 tasks, 2 students solved only one task, and three students only two tasks. Task no. 1 and task no. 2 were solved by 16 students, and tasks 2 and 3 by 14 students. All tasks were solved by 10 st - Advertising on television
A television station claims about its broadcasting schedule that advertising takes up 76 minutes of broadcasting during the whole day and is broadcast at random intervals. a) what is the probability that if you turn the television to this station, it will - Preventive examination 2.8% of the population suffers from disease XY. A preventive examination identifies 5.1% of healthy individuals as sick, and 91.4% of those examined who are actually sick are also identified as sick. What percentage of examined individuals is identified a
- Function graph intercepts
Draw the graph of the function y = -2x + 3. Calculate the coordinates of the intersections of the function's graph with the x and y axes. - Residents
In a college dormitory, 1/10 of the residents are juniors, and 2/5 of the residents are sophomores. What fraction of the students at the dormitory are juniors and sophomores? - Club football tennis The sports club has 302 members. Ten times more members play soccer than tennis. Just one of the sports (F and T) is played by 222 members. Eighty-two members do not play football. How many members of the club play football? How many members play tennis?
- Senior students
There are 7,000 students at Mountain High School, and 2/7 of these students are seniors. If 2/5 of the seniors favour the school forming a debate team and 3/8 of the remaining students (non-seniors) also favour forming a debate team, how many students do - 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 - Conditional probability
Suppose a batch contains ten items, of which four are defective. Two items are drawn at random from the batch, one after the other, without replacement. What is the probability that: I) Both are defective? Ii) Is the second item defective? - Medical trail
In a medical trial, there were 80 patients. 44 received treatment A, 50 received treatment B, and 20 received both treatment A and treatment B. How many patients did not undergo any treatment? - Intersection of Q2 with line
The equation of a curve C is y=2x² - 8x +9, and the equation of a line L is x + y=3. (1) Find the x-coordinates of the points of intersection of L and C. (ii) show that one of these points is also the - Box of donuts
Elizabeth brought a box of donuts to share. There are two dozen (24) donuts in the box, all identical in size, shape, and color. Six are jelly-filled, ten are lemon-filled, and eight are custard-filled. You randomly select one donut, eat it, and select an
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