Boolean algebra - practice problems

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 53

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
Suspicion 82035
At the time of the theft, 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?
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?
Probability 81591
We roll the dice three times. Calculate the probability of getting an even number on the first, second, or third toss.
Probability 80785
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 71174
Find the probability that one will fall at least once in three rolls.
(non-equivalence) 69034
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
Probability 68594
What is the probability that any two-digit number a) is divisible by five b) is it not divisible by five?
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?
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 25% drink both. What is the probability that a person chosen at random will drink neither tea nor coffee?
Probability 59493
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
Children 58031
The children talked about how they spent the holidays at school. 2/3 of them were on holiday with their parents. There were ten children by the sea, which is 5/8 of those who were on vacation. How many children are in the class of children?

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