Answer each question Provethat P ( EF c ) P ( E ) P ( EF) ) Consider a sample of size 3 drawn in the following manner We start with an urn containing 5 white and7redballs Ateachstage, aballisdrawn,anditscolor isnoted Theballisthenreturned to the urn, along with an additional ball of the same color Find the probability that the sample will contain exactly 0whiteballs 1whiteball 3whiteballs 2whiteballs Imagine you are a financial analyst at an investment bank According to your research of publicly traded companies, 60 of the companies that increased their share price by more than 5 in the last three years replaced their CEOs during the period Atthesametime,only35 ofthecompaniesthatdidnotincreasetheir sharepricebymorethan 5 in the same period replaced their CEOs Knowing that the probability that the stock prices growby more than 5 is 4 , find the probability that the shares of a company that fires its CEO will increase by more than 5 Let X be the winnings of a gambler Let p ( i ) P ( X i )and suppose that p (0) 1 3 p (1) p ( 1) 13 55 p (2) p ( 2) 1 11 p (3) p ( 3) 1 165 Compute the conditional probability thatthegamblerwins i,i 1 , 2 , 3,giventhathewinsapositive amount A ball is drawn from an urn containing 3 white and 3 black balls After the ball is drawn, it is replaced andanotherballisdrawn Thisprocessgoesonindefinitely Whatistheprobabilitythatofthefirst 4 balls drawn, exactly 2 are white

The Answer is in the image, click to view ...

Question: Answer each question. Provethat P ( EF c )= P ( E ) P ( EF) ). Consider a sample of size 3 drawn in

Answer each question.

ProvethatP(EF^c)=P(E)P(EF)).
Consider a sample of size 3 drawn in the following manner: We start with an urn containing 5 white and7redballs. Ateachstage, aballisdrawn,anditscolor isnoted.Theballisthenreturned to the urn, along with an additional ball of the same color.Find the probability that the sample will contain exactly.
1. 0whiteballs;
2. 1whiteball;
3. 3whiteballs;
4. 2whiteballs.
Imagine you are a financial analyst at an investment bank.According to your research of publicly- traded companies, 60% of the companies that increased their share price by more than 5% in the last three years replaced their CEOs during the period. Atthesametime,only35%ofthecompaniesthatdidnotincreasetheir sharepricebymorethan 5% in the same period replaced their CEOs.Knowing that the probability that the stock prices growby more than 5% is 4%, find the probability that the shares of a company that fires its CEO will increase by more than 5
LetXbe the winnings of a gambler.Let p(i)=P(X= i)and suppose that p(0)=1/3;p(1)=p(1)=13/55;p(2)=p(2)=1/11;p(3)=p(3)=1/165.Compute the conditional probability thatthegamblerwinsi,i=1,2,3,giventhathewinsapositive amount.
A ball is drawn from an urn containing 3 white and 3 black balls.After the ball is drawn, it is replaced andanotherballisdrawn.Thisprocessgoesonindefinitely.Whatistheprobabilitythatofthefirst 4 balls drawn, exactly 2 are white?