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Discrete Mathematics
Q3 X people are chosen from a volley ball team (Take a value of X by yourself, possibly that number must be close to a number of volley ball team members).
a) How many ways are there to choose Y people to take them to ground(Take value of y by yourself less than x)
b) How many ways are there to assign Z positions by selecting players from X people.(Take Z value by yourself and previous X value.)
c) Of the X people T are women. How many ways are there to choose W players to take them to the field if at least 1 of these players must be a women
a) How many ways are there to choose Y people to take them to ground(Take value of y by yourself less than x)
b) How many ways are there to assign Z positions by selecting players from X people.(Take Z value by yourself and previous X value.)
c) Of the X people T are women. How many ways are there to choose W players to take them to the field if at least 1 of these players must be a women
Discrete Mathematics
Q2 Draw any three graphs (Take help from book, but DO NOT copy paste any graph from examples or exercise. Your graphs must be random and all must neither be euler nor all non-euler)
a) Figure out Euler graph from these three graphs.
b) Write down the Euler path of these graphs.
c) If not Euler, provide the reason.
a) Figure out Euler graph from these three graphs.
b) Write down the Euler path of these graphs.
c) If not Euler, provide the reason.
Discrete Mathematics
Q1 Draw any balance rooted tree having nodes from “ a to i”.
a) Find the level of each vertex in the drawn tree.
b) Find the height of this tree.
c) Which vertices are descendants of node “g”.
a) Find the level of each vertex in the drawn tree.
b) Find the height of this tree.
c) Which vertices are descendants of node “g”.
Discrete Mathematics
In a physics class 40 children had forgotten to bring their physics book,34 had forgotten to do their homework. The teacher asked to borrow the physics book from some one at once. 48 childrens left the room. Draw a Venn diagram and find how many children had forgotten both?
Discrete Mathematics
In a certain group of 15 students, 5 have graphics calculators and 3 have a computer at home (one student has both). Two of the students drive themselves to college each day and neither of them has a graphics calculator nor a computer at home. A student is selected at random from the group.
Let G represent the event “the student has a graphics calculator”, H represent the event “the student has a computer at home”, D represent the event “the student drives to college each day”
Represent the information in this question by a Venn diagram. Use the above Venn diagram to answer the questions.
(a)Find the probability that the student either drives to college or has a graphics calculator.
Discrete Mathematics
Find the minimum number n of integers to be selected from S = {1, 2,..., 9} so that: (a) The sum of
two of the n integers is even. (b) The difference of two of the n integers is 5.
two of the n integers is even. (b) The difference of two of the n integers is 5.
Discrete Mathematics
3. A certain medical disease occurs in 1% of the population. A simple screening procedure is available and in 8 out of 10 cases where the patient has the disease, it produces a positive result. If the patient does not have the disease there is still a 0.05 chance that the test will give a positive result. Find the probability that a randomly selected individual:
(a) Does not have the disease but gives a positive result in the screening test
(b) Gives a positive result on the test
(c) Nilu has taken the test and her result is positive. Find the probability that she has the disease.
(a) Does not have the disease but gives a positive result in the screening test
(b) Gives a positive result on the test
(c) Nilu has taken the test and her result is positive. Find the probability that she has the disease.
Discrete Mathematics
Robyn decides to organize a hiking trip and invites her friends - Dylan, Linda and Dominic to join her. On the days leading to the hike, her three friends say the following:Two Days Before the hike:Dylan: Dominic is going to the hike. Dominic: Linda is not going to the hike.Linda: Dylan will go to the hike if, and only if, I do.The Day Before the hike:Dylan: Linda will go to the hike if, and only if, I don't go. Dominic: An even number out of the three of us are going to the hike.Linda: Dylan is going to the hike.The Day of the hike:Dylan: It is not yet 2020. Dominic: Dylan will go to the hike if, and only if, I do.Linda: At least one of the three of us is not going to the hike. Robyn also knows that out of Dylan, Dominic, and Linda:One of them never lies.One lies on days of the month that are divisible by 2, but is otherwise truthful.The remaining one lies on days of the month that are divisible by 3, but is otherwise truthful.Can you figure out who is going to attend?
Discrete Mathematics
Robyn decides to organize a hiking trip and invites her friends - Dylan, Linda and Dominic to join her. On the days leading to the hike, her three friends say the following:Two Days Before the hike:Dylan: Dominic is going to the hike. Dominic: Linda is not going to the hike.Linda: Dylan will go to the hike if, and only if, I do.The Day Before the hike:Dylan: Linda will go to the hike if, and only if, I don't go. Dominic: An even number out of the three of us are going to the hike.Linda: Dylan is going to the hike.The Day of the hike:Dylan: It is not yet 2020. Dominic: Dylan will go to the hike if, and only if, I do.Linda: At least one of the three of us is not going to the hike. Robyn also knows that out of Dylan, Dominic, and Linda:One of them never lies.One lies on days of the month that are divisible by 2, but is otherwise truthful.The remaining one lies on days of the month that are divisible by 3, but is otherwise truthful.Can you figure out who is going to attend?
Discrete Mathematics
b) In a large city, 8% of the inhabitants have contracted a particular disease. A test for this
disease is positive in 80% of people who have the disease and is negative in 80% of people
who do not have the disease. What is the probability that a person for whom the test result
is positive has the disease?
disease is positive in 80% of people who have the disease and is negative in 80% of people
who do not have the disease. What is the probability that a person for whom the test result
is positive has the disease?
