Wednesday, June 15, 2016

Inclusion exclusion problems - set theory




1.      A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of three popular options air conditioning (A) , radio (R) and power windows (W) were already installed. The survey found
15 had air conditioning
12 had radio
11 had power windows
5 had air conditioning and power windows
9 had air conditioning and radio
4 had radio and power windows
3 had all three options
Find the number of cars that had
a.      Only power windows
b.      Only air conditioning
c.       Only radio
d.      Radio and power windows but not air conditioning
e.      Air conditioning and radio but now power windows
f.        Only one of the options
g.      Atleast one of the option
h.      None of the options

2.      A survey among 1000 people, 595 are democrats, 595 wear glasses and 550 like ice cream, 395 of them are democrats who wear glasses, 350 of them are democrats who like ice cream. 400 of them wear glasses and like ice cream and 250 all the three.
a.      How many of them are not democrats , do not wear glasses and do not like ice creams
b.      How many of them are democrats who do not wear glasses and do not like ice cream?

3.      It is known that in university 60% of professors play tennis, 50% of them play bridge, 70% jog, 20% play tennis and bridge, 40% play bridge and jog, 30% play tennis and jog. Find the percentage of professors who play tennis, bridge and jog?

4.      In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. if 14 liked product A and , 12 liked products C and A, 14 liked products B and C and 8 liked all the three products. Find how many liked product C only.

5.      In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee. 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee.

6.      In a group of 100 students, 100 students know hindi, 50 know English and 25 know both. Each of the students knows either English or hindi. How many students are there in total?

7.      A college rewarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?

8.      In a committee 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak atleast one of these two languages?

9.      A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 like product B what is the least number that must have liked both products?

10.  There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C1, 50 to chemical C2 and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to
a.      Chemical C1 but not C2
b.      Chemical C2 but not C1
c.       Chemical C1 or C2

No comments:

Post a Comment