Question 6.

Suppose Bill and Jane now decide to bet on various possible outcomes of a table tennis tournament consisting of 7 games.The conditions of the bet are as outlined in the following table.

Tournament Result

Payment

Bills Winnings

Bill winsexactly 4 games out of 7

Jane pays Bill

$V40

$V40

Bill wins exactly5 out of the7 games

Jane pays Bill

$W20

$W20

Billwins exactly 6 out of the7 games

Jane pays Bill

$G55

$G55

Billwins all7 games

Jane pays Bill

$M40

$M40

Otherwise

Bill pays Jane

$N20

-$N20

(a) We can define a discrete random variable X to be the amount Bill wins in a particular tournament.

Calculate the total expected winnings for Bill by completing the table below. (Hint: You will fill out the probability column based on the results of question 5 ).

Tournament Result

Bill Winnings=x

P(X=x)

x P(X=x)

Bill winsexactly 4 games out of 7 games

$V

Billwins exactly 5 out of the7 games

$W

Billwins exactly 6 out of the7 games

$G

Billwins all7 games

$M