Intersection of sets - practice problems
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 171
- Richard
Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number? - X intercept
Given: 3y+2x=-6 Calculate the X-intercept. - Library and gym
In a town, 7/8 of the population has a library card, and 3/4 has a gym membership. What fraction of the population has either a library card or a gym membership? - And or logic
If A and B are events with P(A)=0.3, P(A OR B)=0.76, and P(A AND B)=0.04, find P(B). Enter your answer in decimal form, rounded to one place.
- Three 241
Three-fifths of the t-shirts in a t-shirt shop are blue. Five-eights of those T-shirts are on sale. One-third of the blue of the blue shirts that are on sale are size medium. What fraction of the shop's blue T-shirts are on sale and size medium? - And - or probability rules
Given P(A)=0.4, P(B)=0.56, and P(A and B)=0.274, find the value of P(A or B), rounding, if necessary. - Exactly 4
Exactly 1/6 of the kids are playing on the playground. Exactly 3/5 of the kids are playing soccer. Jack adds 1/6 + 3/5 to find the total fraction of kids at the park playing on the playground or playing soccer. Is he correct? - Five roommates
Five roommates will move into a house with four bedrooms: one double room and three single rooms. The five roommates propose that they draw names to determine the order in which they pick the bedrooms, assuming that the first three names drawn will choose - Ruben
Ruben owns a restaurant. He likes to keep track of everything customers are buying. His top 3 sellers are sandwiches, salads, and pizza. He knows that 1/3 of his customers buy a sandwich, 1/2 buy a salad, and 1/4 buy a pizza. What fraction of customers bu
- Three sets
Of 240 students, 173 are on the honor roll, 48 are members of the varsity team, and 36 are on the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the vars - 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 - Here are 2
Here are two sets: A:={{1,2},{1,4},{2,4}} and B:={{1,4},{1},{2},{4,2}}. How large is |A∩B| - Intersection of two sets
A = {a, b, c, d, e, f, g, h, i}, B = { d, g, f, k, j, a}, find A ∩ B. - Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8|
- Testing students
Giving a test to a group of students, the grades and gender are summarized below. Grades and Gender ; A; B ; C ; Total Male; 20; 6; 19 ; 45 Female ; 17; 18; 13; 48 Total; 37; 24; 32; 93 If one student is chosen at random, a) Find the probability that the - Rectangular 83244
The rectangular pool has dimensions of 25 meters and 12.5 meters. A 2-meter wide path surrounds the pool. How many square meters of tiles are needed to pave a sidewalk? - Students 83223
There are 24 students in the class. Eleven of them have a dog at home. The tiny rodent has 15 of them. No animal has 5 students at home. How many students have 2 pets at home? - Determine 83003
Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common. - Parametrically 82990
Calculate the sum of the x-coordinates of the intersections of the circle given by the equation (x - 1)²+ y² = 1 and the line given parametrically x = t, y = t , where t∈R.
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