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

## Answer: P(A1 ? A2) = 0.35Solution:A1 : '' awarded project 1''A2 : ''awarded project 2''A3: ''awarded project 3''In set theory we write the union of events A and B as A?B.A?B means that the event A occurs,event B occurs or either both events occurs at the same time.The probability is given by the equation :P(A?B) = P(A) + P(B) - P(A?B) (1)Where the event (A?B) is the event where A and B occur at the same timeand P(A?B) is the probability of (A?B)Using the equation (1) :P(A1 ? A2) = P(A1) + P(A2) - P(A1?A2)P(A1 ? A2) = 0.22 + 0.25 - 0.12P(A1 ? A2) = 0.35

#### Topics

Probability Topics

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M1

Md. 1.

April 17, 2021

find the conditional probability and interpret the probability

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University of Ottawa

#### Topics

Probability Topics

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