A group of smallbusiness owners consists of 254 men and 96 w

A group of small-business owners consists of 254 men and 96 women. 100 people in this group consult an account. 160 people in this group consult a financial planner. 92 people in this group consult both an accountant and a financial planner.   A person is selected at random from this group. What is the probability (to 3 decimal places) that this person

is a woman?

consults a financial planner?

consults an accountant or a financial planner?

Solution

Let Event A : People who consult an accountant

Let Event B : People who consult a financial planner

P(A) = 100/(254+96) = 0.2857

P(B) = 160/(254+96) = 0.4571

P( A AND B) = 92/(254+96) = 0.2629

i)

P(Person is a woman) = 96/(254+96) = 0.274 Answer

ii)

P(B) = 160/(254+96) = 0.457 Answer

iii)

P(A OR B) = P(A) + P(B) - P( A AND B)

= 0.2857 + 0.4571 - 0.2629

= 0.480 Answer