Check the venn diagram of the problem.
let the total number of the clients be 100.
since there are 11 clients with both cats and dogs,
there are 32-11=21 clients with dogs but not cats
and 25-11=14 clients with cat but not dogs.
The number of clients with neither dogs nor cats is given by:
100-(21+11+14)=100-46=54
so we have the following:
P(C)=25/100=0.25
P(D)=32/100=0.32
P(C∩D)=P(D∩C)=11/100=0.11
we also have the formula P(A|B)=P(A∩B)/P(B), the formula of conditional probability
now we check each choice:
1. P(C|D)=P(C∩D)/P(D)=0.11/0.32=0.34
2. P(D|C)=P(D∩C)/P(C)=0.11/0.25=0.44
3 and 4 are already checked, and they are true
5. by 1 and 2, not true
Answer: 2, 3, 4 are True