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The following formulas have been abbreviated based on the common abbreviation rules. Follow the steps below and translate the formulas into good English.
· Step 1: Re-add the omitted brackets.
· Step 2: If necessary, convert them into some other logically equivalent formula
so as to make it more readable. Write out the rule(s) you use for conversion.
· Step 3: Translate the formulas into `good' English. Try to make your translation as brief/understandable as possible. (For instance, `John and Bill are coming' is better than `John is coming and Bill is coming.')
p: John wants to come to the class.
q: John will come to the class today.
r: John audits the class.
s: John is enrolled in the class.
Hint:
`No matter whether John is going or not, I'm going.' is the translation for (j à i) ^ (⌐j à i),
in which j = John is going, i = I'm going.)
Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses.
Find the number N of students in a dormitory given the data:
12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D,
20 take B, 7 takeAand C, 3 takeC and D, 3 take A, C,D,
20 take C, 4 takeAand D, 3 take A, B,C, 2 take all four,
8 take D, 16 takeB and C, 2 take A, B, D, 71 take none.
The following contingency table represents the voters’ opinion concerning a new tax
reform bill and their level of income.
Levels of Income
Opinion Low Medium High
For 213 203 182
Against 138 110 154
Apply chi-square (χ2
) test to examine whether the opinion of people on new tax bill is
independent from their income level. [Table value of chi- square (χ2
) at 5% level of
significance and for 2 degrees of freedom is 5.99
Draw a simple, undirected graph yourself, the vertices are connected with each other including 8 vertices and 14 edges. Find the shortest path from two arbitrary vertices:
a) The weight of each edge is 1.
b) Self-weighting for edges
Mr. X is known to hit the target in 4 out of 5 shots, where as Mr. Y is known to hit the target in 3 out of 5 shots. Find the probability that both will hit the Target
There are 10 teams. Each team plays another team each week for 15 weeks. The team with the higher score that week wins the game and gets a win. The team with the lower score in the matchup gets a loss. At the end of the season the teams with the best 6 win/loss records advance to the next round and the teams with the four worst win/loss records are eliminated.
What is the probability of the four teams with the highest number of total points scored getting eliminated? Also, what are the chances of the team with the most points scored coming in 10th place? Bonus if you know the probability of both things happening!
A production facility contains two machines that are used to rework items that are initially defective. Let 𝑋 be the number of hours that the first machine is in use and let 𝑌 be the number of hours that the second machine is in use, on a randomly chosen day. Assume that 𝑋 and 𝑌 have a joint probability density function given by 𝑓(𝑥) = { 3 2 (𝑥 2 + 𝑦 2 ) 0 < 𝑥 < 1 𝑎𝑛𝑑 0 < 𝑦 < 1 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. a. What is the probability that both machines are in operation for less than half an hour?
A school organized a book fair and in this book fair a book seller is selling his books under the following rules:
There are three different packages available.
First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack.
How many packs should be made to maximize book fair profits?
What will the profit be?
There are 4 traffic lights along the road, each prohibits further movement of the car with a probability of 0.5. Find the
distribution of the number of the traffic lights that car passed to the first stop. What is the variance of the random
variable?
CS. The efficiency rating of 155 faculty members of a certain college was taken and is shown below
Classes f
73-75 2
76-78 6
79-81 12
82-84 16
85-87 18
88-90 39
91-93 36
94-96 21
97-99 5
Determine the value of
1. P36
2. D5
3. Q3
