In a survey conducted on a group of 1000 people it is found that 40% buy product A, 20% buy - Maths - Probability

Question

In a survey conducted on a group of 1000 people it is found that
40% buy product A, 20% buy product B, and 10% buy Product C, 5% buy
products A and B, 3% buy products B and C and 4% buy products A and
C If 2% of the group buy all the three products, then find the
number of people who buy i) product A only ii) atleast one of the
products A, B or C ​​

Neha Sethi · Accepted Answer

Dear student
Let P ,Q and R denote the sets of people buying product A,B,Crespectively
Let U be the universal set
ThennP=40%of 1000=400nQ=20% of 1000=200nR=10%of 1000=100nP∩Q=5% of 1000=50,nQ∩R=3% of 1000=30nR∩P=4% of 1000=40nP∩Q∩R=2% of 1000=20nU=10001Required number=nP∩Q'∩R'=nP∩Q∪R'=nP-nP∩Q∪R=nP-nP∩Q∪P∩R=nP-nP∩Q+nP∩R-nP∩Q∩R=400-50+40-20=3302Atleast  one of the products A ,B or CnP∪Q∪R=nP+nQ+nR-nP∩Q-nQ∩R-nR∩P+nP∩Q∩R=400+200+100-50-30-40-20=700-140=560
Regards