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Probability with Applications in Engineering, Science, and Technology

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 $P\left(A_{1}\right)=.22, P\left(A_{2}\right)=.25, P\left(A_{3}\right)=.28, P\left(A_{1} \cap A_{2}\right)=.11$ $P\left(A_{1} \cap A_{3}\right)=.05, P\left(A_{2} \cap A_{3}\right)=.07, P\left(A_{1} \cap A_{2} \cap A_{3}\right)=.01 .$ Express in words each of the following events, and compute the probability of each event:

(a) $A_{1} \cup A_{2}$

(b) $A_{1}^{\prime} \cap A_{2}^{\prime}$

(c) $A_{1} \cup A_{2} \cup A_{3}$

(d) $A_{1}^{\prime} \cap A_{2} \cup A_{3}$

(e) $A_{1}^{\prime} \cap A_{2}^{\prime} \cap A_{3}$

(f) $\left(A_{1}^{\prime} \cap A_{2}^{\prime}\right) \cup A_{3}$