19MA601 : Foundation of Mathematics - Community Organization - Mathematics Assignment Help

Assignment Task :

Exercise 2.1 

Suppose that a room contains n people. What is the probability that at least two of them have a birthday on same month? Make a plot of probability vs number of people and find out for how many people does the probability becomes greater than 0.5 and 0.9. 

Exercise 2.2 

Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent wear a ring and 30 percent wear a necklace. If one of the students is chosen randomly, what is the probability that this student is wearing 

a) a ring or a necklace? 

b) a ring and a necklace? 

Exercise 2.3 

A certain town with a population of 100,000 has 3 newspapers: I, II, and III. The proportions of townspeople who read these papers are as follows 

• I: 10 percent 

• II: 30 percent 

• III: 5 percent 

• I and II: 8 percent 

• I and III: 2 percent 

• II and III: 4 percent 

• I and II and III: 1 percent 

Now answer the following questions:- 

a) Find the number of people who read only one newspaper. 

b) How many people read at least two newspapers? 

c) If I and III are morning papers and II is an evening paper, how many people read at least one morning paper plus an evening paper? 

d) How many people do not read any newspapers? 

e) How many people read only one morning paper and one evening paper? 

Exercise 2.4 

A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children, 2 have four children, and 1 has five children. 

a) If one of these families is chosen at random, what is the probability it has i children, i = 1, 2, 3, 4, 5? 

b) If one of the children is randomly chosen, what is the probability that child comes from a family having i children, i = 1, 2, 3, 4, 5? 

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