# Intersection of sets - practice problems

#### Number of problems found: 127

- Conditional probability

Suppose a batch contains 10 items of which 4 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) the second item is defective? - Medical trail

In a medical trail, there were 80 patients. Twenty-four received treatment A, 30 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. 6 are jelly-filled, 10 are lemon-filled, and 8 are custard-filled. You randomly select one donut, eat it, and select a - Three 192

Three separate containers each have one purple marble and two blue marbles. One marble is chosen from each box. Find the probability of choosing a blue marble from each box. - Rafael

Rafael has three squares. The first square has a side length of 2 cm. The second square has a side length of 4 cm and its vertex is placed in the center of the first square. The last square has side length 6 cm and its vertex is placed in the center of th - The following

The following data represents the number of cases of coffee or filters sold by four sales reps in a recent sales competition. Sales Person; Gourmet; Single Cup; Filters; Total Connor; 142; 325; 30; 497 Paige ; 42; 125; 40; 207 Bryce ; 9; 100; - 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 - Conditional 73664

I roll a 7-wall dice. What is the conditional probability that three fell if an odd number fell? - Probability 73654

We roll two dice. One is 6-walled, and the other is 8-walled. What is the probability that at least one unit will fall? - Two-thirds 73104

The company has 120 employees, two-thirds of whom are women. Of the women, only a quarter speak both English and German. How many women talk in English and German? - 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 in the exams while among the female 50% failed. (a) present this using a probability tree diagram (b) determine probabilit - Freezer 70664

There are a total of 38 ducks in the freezer. Of these, 24 weigh more than 1.2, and 22 ducks weigh less than 1.5. How many ducks weigh more than 1.2 and less than 1.5 kg? - 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 - Probability 68584

There are five whites and nine blacks in the destiny. We will choose three balls at random. What is the probability that a) the selected balls will not be the same color, b) will there be at least two blacks between them? - Probability 68574

The target is divided into three zones. The probability of a shooter hitting the first band is 0.18, the second band 0.2, and the third band 0.44. What is the probability that a) hits the target, b) miss the target? - Cancer in woman population

In a certain 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 had breast cancer, smokes or both? - Operations 66444

Consider an experiment with a dice. Let us define the random events A={at most 3}, B={roll more than 1}, C={roll 2, 3, 4}. Determine the random event D that is given by the operations A∪B \ B∪C - 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 - All multiples

Set A is a set of all multiples of 2 and set B is a set of all multiples of 3. If the P (A)=0.6 and P (B)=0.3. Find P (AUB).

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