In Exercise 13, is any Ai independent of any other Aj? Answer using the multiplication p...

In Exercise 13, is any A_i independent of any other A_j? Answer using the multiplication property for independent events.

Reference exercise- 13

A computer consulting firm presently has bids out on three projects. Let A_i = { awarded project i}, for i = 1,2,3, and suppose that P(A₁) =.22, P(A₂) = .25, P(A₃) = .28, P(A₁∪A₂) = .11,P?(A₁∪A₃)= .05, P(A₂∩A₃) = .07, P(A₁∩A₂∩A₃)= .01. Express in words each of the following events, and compute the probability of each event:

a. A1∩A2

b.A′₁∩A’₂[Hint:( A₁∪A₂) ′= ( A′₁∩A′₂]

c.A₁∪A₂∪A₃

d. A′₁∩A′₂∩A’₃

e. A′₁∩A′₂∩A₃

f.( A′₁∩A′₂) ∪A₃