Boolean algebra - practice problems - page 2 of 4
Instructions: For each problem, solve carefully and show your complete working.Number of problems found: 67
- Drinks
In a country, 65% of people drink coffee, 50% drink tea, and 25% drink both. What is the probability that a person chosen at random will drink neither tea nor coffee? - We are planting
We are planting 2 types of roses (white and red). Experience shows that the probability of a red rose taking root is 0.7. A total of 5 seedlings are planted. What is the probability that: a) the first 2 will be red and the next 3 white? b) all will be red - Three languages 2
Participants of a congress may present their contributions in English, Italian, or Spanish. Each of the 120 participants knows at least two of these languages, and 10 participants speak all three languages. English and Spanish is spoken by exactly as many - Bridge cards
Determine the probability of a random event out of 10 randomly selected bridge cards. There will be at least three aces. Note This is a team game, with 52 cards in the deck, of which four aces. - AND-NOT-AND
If P is the set of multiples of 2, Q is the set of multiples of 3, and R is the set of multiples of 7, the following integers will be in P and Q but not in R: A=−54 B=−50 C=42 D=100 E=252 - Vacation class children
The children talked about how they spent the holidays at school. 2/3 of them were on holiday with their parents. Ten children went to the seaside, which is 5/8 of those who were on vacation. How many children are in the class? - Three robots
In a workshop, three robots, Q, R, and S, are employed to make chairs Robot Q makes 25% of the chairs Robot R makes 45% of the chairs The remaining chairs are made by Robot S Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 - Two fertilizers
Jason is testing two fertilisers, Grow Well and Green Grow, on 50 tomato plants of the same variety planted in identical conditions. He applied Grow Well to 25 plants and Green Grow to the other 25. After four weeks, he measured the heights of the plants - School student
The probability that a school student has a skateboard is 0.34, the probability that he has a bicycle is 0.81, and the probability that he has a skateboard and a bicycle is 0.22. What is the probability that a randomly selected student has a skateboard or - Divisibility indirect proof
Prove indirectly: No odd natural number is divisible by four. - Truth table tautology
Use the truth table to evaluate the truth of the compound statement (a) [P ∧ (Q ∨ R)] ⇔ [(P ∧ Q) ∨ (P ∧ R)] (b) ¬(P ⇒ ¬Q) ⇒ (¬P ∧ Q) and decide each time whether it is a tautology or A contradiction. - The vaccination
The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated and more likely to be infected? Consider N = 10,000 inhabitants and K = 1,000 infected. b. How many times more likely are unvacci - Quadrant four
Which point is located in Quadrant IV? A coordinate plane. A(-8, 6) B(-8, -6) C(8, -6) D(8, 6) - 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 - Calculate: 2
Calculate: 1. Write the given sets as intervals, represent graphically: {x ∈ R; 2< x ≤ 5} = {x ∈ R; 3 ≥ x} = {x ∈ R+; x < 4} = {x ∈ R; x < 4 ∧ x ≥ -1} = 2. List all elements of the following sets, write into set brackets: A = { x Є N; x ≤ 5 } A = B - Crimson Lynx
Captain Emily has a ship, the H. M. S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves. If her ship hasn't already been hit, Captain Emily has a probability of 3/5 of hitting the pirate ship. If her sh - Mastering
The student masters the subject matter for the exam in Czech to 98%, from Math to 86%, and from Economics to 71%. What is the probability that he will fail in Math and that others will succeed? - Four children
What is the probability that in a family with four children, there are: a) at least three girls b) at least one boy, If the probability of a boy is 0.51? - Number zero puzzle
I think of a number. When it is substituted into the expression (x − 4)(2x − 1), the result is zero. What could the number be? - 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.
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