2) In the United States, 56% of all children get an allowance and 41% of all children get an allowance and do household chores. 15% of all children do neither. what is a) P (household chores only)

0.46

Step-by-step explanation:

Let A be the no of children who get an allowance and B the no of children who get both allowance and do household chores.

Given that P (A) = 0.56 and P (AB) = 0.41

Also P (A'B') = 0.15 where A' represents the complement of A and B' is complement of B.

We know that total children can be classified into 4 disjoint and exhaustive groups as

A-B, AB, B-A and A'B'

Consider A, A is union of (A-B) U (AB) (two disjoint sets)

Hence P (A) = P (A-B) + P (AB)

0.56 = P (A-B) + 0.41

Hence P (A-B) = 0.15

i. e. Total probability = 1

i. e. 0.56-0.15+P (B-A) + P (A'B') = 1

Hence P (B-A) = 1-0.41-0.15 = 0.46

P (household chores only) = 0.46