Boolean algebra - practice problems - page 3 of 4
Instructions: For each problem, solve carefully and show your complete working.Number of problems found: 67
- Specialist hiring probability
A private company will hire two IT specialists. Thomas is among the five registered candidates. What is the probability that he will not be accepted? - Hospital death probability
Statistically, in a city of 100,000 inhabitants, 600 people die in one year. During the year, 2,000 people received hospital treatment, and 120 of them died there. Calculate the probability that a citizen who comes to the hospital for treatment will die t - Birthday paradox
How large must a group of people be so that the probability of at least two people sharing a birthday is greater than 90%? - Homework probability
Today, one-fifth of 30 students still need to complete a homework assignment. What is the teacher's probability of randomly selecting a pupil with homework during the check? - Double probability
The probability of success of the planned action is 60%. What is the probability that we will achieve success at least once if this action is repeated twice? - 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%? - Percents from percent
How much is 13% of 20% of 500 greater than 8% of 14% of 200? - The university
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in the - Sick days
In Canada, there are typically 261 working days per year. There is a 4.9% chance of an employee taking a sick day. What is the probability an employee will use 17 OR MORE sick days in a year? - Snow White 2019 MO Z7
Snow White with her seven dwarfs gathered pinecones for a bonfire. Snow White said that the number of all pinecones is a number divisible by two. The first dwarf stated that it is a number divisible by three, the second dwarf said that it is a number divi - School trip
On a school trip, 17 of the 28 children bought ice cream or chocolate in a candy store. Twelve children bought chocolate, and nine children bought ice cream. How many children bought ice cream and chocolate? How many children did not buy ice cream? How ma - Kocour coin values
In Kocourkov, they use coins with only two values expressed in Kocourkov crowns by positive integers. With a sufficient number of such coins, it is possible to pay any integer amount greater than 53 cats’ crowns accurately and without return. However, we - Z9 – I – 4 MO 2019
Matúš landed with a parachute on an island inhabited by two kinds of natives: the Honest ones, who always tell the truth, and the Liars, who always lie. Before landing he glimpsed in the distance a harbour, to which he intended to get. At the first crossr - Records
Records indicate 90% error-free. If eight records are randomly selected, what is the probability that at least two records have no errors? - Number divisor proof
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - Test 10 questions
A test has 10 questions with multiple-choice answers. For the choice of the correct answer there are four options A, B, C, D, where always one of them is correct. How many are there all different possibilities for answers in this test, a) if its taker ans - Intersect and conjuction
Let U={1,2,3,4,5,6} A={1,3,5} B={2,4,6} C={3,6} Find the following. 1. )AUB 2. )A'UB' - Three shooters
Three shooters each fire once at the same target. The first hits the target with a probability of 0.7, the second with 0.8, and the third with 0.9. What is the probability of hitting the target: a) exactly once? b) at least once? c) at least twice? - The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor; no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - MO Z9-I-3 2018
In our town there are three cinemas, which are named according to the compass points. About their opening hours it is known that: • every day at least one cinema is open, • if the southern cinema is open, then the northern cinema is not open, • the northe
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