In class of 300 house wives, it was discovered that 100 read magazine A, 200 read magazine B and 156 read magazine C. It was further discovered that 48 read A and B, 60 read B and C and 52 read A and C.all read at least one Find
a) the number of house wives that read all three
b) the number of house wives that read at least two
c) the number of house wives that read only one
To solve this problem, we can use the principle of inclusion-exclusion.
a) The number of housewives that read all three magazines can be found by adding up the number of housewives who read A, B, and C, and then subtracting the number of housewives who read at least two.
Number of housewives that read all three = 48
b) To find the number of housewives that read at least two magazines, we need to add the number of housewives who read A and B, B and C, and A and C. However, we have counted the housewives who read all three twice (once in each combination). So, we need to subtract the number of housewives who read all three.
Number of housewives that read at least two = (48 + 60 + 52) - 48 = 112
c) To find the number of housewives that read only one magazine, we need to subtract the number of housewives who read at least two magazines from the total number of housewives who read each magazine.
Number of housewives that read only one = (100 + 200 + 156) - 112 = 344
So, the answers are:
a) 48 housewives read all three magazines.
b) 112 housewives read at least two magazines.
c) 344 housewives read only one magazine.