Boolean algebra - practice problems
Boolean algebra is a branch of mathematics dealing with variables that have only two possible values: true or false, often represented as 1 or 0. The fundamental operations are AND (conjunction), OR (disjunction), and NOT (negation), along with derived operations like XOR and NAND. Boolean algebra follows specific laws including commutative, associative, and distributive properties, as well as De Morgan's laws. It forms the theoretical foundation of digital electronics and computer science, underlying circuit design and programming logic. Truth tables systematically show all possible outcomes of Boolean operations. Students learn to simplify Boolean expressions and solve logical problems using Boolean algebra.Instructions: For each problem, solve carefully and show your complete working.
Number of problems found: 59
- Defect rate
A manufacturing machine has a 3% defect rate. If 9 items are chosen randomly, what is the probability that at least one will have a defect? - 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. - 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. - Logical and
At a football game, 8/15 of the fans wore team T-shirts. Of those wearing team T-shirts, 1/4 also wore team hats. What fraction game wore both a team T-shirt and a team hat? - Ekene and Amina
The probability that Ekene will be alive in 5 years' time is 3/4, and the probability that his wife Amina will be alive in 5 years' time is 2/5. Find the probability that in 5 years' time: a) both of them will be alive b) only Ekene will be alive - A disease
A disease affects 10% of the individuals in a population, and a sample of 100 people was selected from the population. What is the probability of finding the disease in at least 15 people? - Traffic accidents
Of the total number of traffic accidents, 80% occur in the village and 20% outside the village. If the number of traffic accidents in the village were reduced by 40%, by what percentage would the total number of traffic accidents decrease? - Hotel theft suspicion
At the time of the theft, there were 96 people in the hotel; 61 were beyond suspicion. Of the 47 employees at the hotel, 23 are beyond suspicion. How many guests are not beyond suspicion? - Dice even probability
We roll the dice three times. Calculate the probability of getting an even number on the first, second, or third toss. - 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? - A bag 4
A bag contains 18 balls that differ only in color, 11 are blue, and seven are red. If two balls are picked, one after the other without replacement, find the probability that both are (i) Blue (ii) Of the same color (iii) Of different colors - 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 - 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 the exams, while among the females, 50% failed. (a) present this using a probability tree diagram (b) determine the pr - Probability - on the roll
Find the probability that one will fall at least once in three rolls. - Non-equivalence
Write the function logical disagreement – entire sum (non-equivalence) F = A ⊕ B (EXL –OR) in a different notation and draw a Karnaugh map. Use NAND elements to implement the above function if you only have variables A and B - Number divisibility probability
What is the probability that any two-digit number a) is divisible by five b) is it not divisible by five? - Target zone probability
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? - 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).
- Book Store
The Mabini Book Store (MBS) is reducing the prices of Mathematics books for promotion. The store has 6 Algebra books, 6 Geometry books, and 5 Statistics books to be arranged on a shelf. Books of the same kind are to be placed beside each other. How many w - 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?
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