(Solved): Problem 3) (30 Points) A computer consulting firm presently has bids out on three projects. Let \( ...

Problem 3) (30 Points) A computer consulting firm presently has bids out on three projects. Let \( \mathrm{Ai}=\{ \) awarded project \( \mathrm{i}\} \), for \( \mathrm{i}=1,2,3 \), and suppose that \( \mathrm{P}(\mathrm{A} 1)=.22, \mathrm{P}(\mathrm{A} 2)=0.25, \mathrm{P}(\mathrm{A} 3)=0.28, \mathrm{P}(\mathrm{A} 1 \cap \mathrm{A} 2)=0.11 \), \( \mathrm{P}(\mathrm{A} 1 \cap \mathrm{A} 3)=0.05, \mathrm{P}(\mathrm{A} 2 \cap \mathrm{A} 3)=0.07 \), and \( \mathrm{P}(\mathrm{A} 1 \cap \mathrm{A} 2 \cap \mathrm{A} 3)=0.01 \). Compute the probability of each of the following events: a. \( \mathrm{A} 1 \cup \mathrm{A} 2 \) b. \( \mathrm{A} 1^{\prime} \cap \mathrm{A} 2^{\prime}\left[\right. \) Hint: \( \left.(\mathrm{A} 1 \cup \mathrm{A} 2)^{\prime}=\mathrm{A} 1^{\prime} \cap \mathrm{A} 2^{\prime}\right] \) c. \( \mathrm{A} 1 \cup \mathrm{A} 2 \cup \mathrm{A} 3 \) d. \( A 1^{\prime} \cap A 2^{\prime} \cap A 3^{\prime} \) e. \( A 1^{\prime} \cap A 2^{\prime} \cap A 3 \) f. \( \left(\mathrm{A} 1^{\prime} \cap \mathrm{A} 2^{\prime}\right) \cup \mathrm{A} 3 \) g. \( \mathrm{A} 2 \mid \mathrm{A} 1 \) h. \( \mathrm{A} 2 \cap \mathrm{A} 3 \mid \mathrm{A} 1 \) i. A2 U A3 |A1 j. \( \quad \) A1 \( \cap \) A2 \( \cap \) A3 \( \mid \) A1 U A2 U A3