Question

a certain game consist of rolling a single fair die and pays off as follows: $5 for a $6, $4 for a 5, $3 for a 4 and no payoff otherwise. find the expected winnings for this game

Answer 1

SOLUTION :

• Let X is a random variable shows the winning amount. Here X can take values $5, $4, $3 and $0.

  When a single fair die is rolled the possible outcomes are 1, 2, 3, 4, 5, and 6.

  Out of 6 outcomes, 1 is 6 so when X= $5 then

  P(X=$5) = 1/6

  Out of 6 outcomes, 1 is 5 so when X= $4 then

  P(X=$4) = 1/6

  Out of 6 outcomes, 1 is 4 so when X= $3 then

  P(X=$3) = 1/6

  And

  P(X=$0) = 1- P(X=$5) - P(X=$4) - P(X=$3) = 3/6

  Following table shows calculations for expected winning:

  X	P(X=x)	xP(X=x)
  5	1/6	5/6
  4	1/6	4/6
  3	1/6	3/6
  0	3/6	0
  Total		2

So expected winning is

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