Question

Prizes and the chances of winning in a sweepstakes are given in the table below. Prize Chances $10,000,000 1 chance in 200,000,000 $350,000 1 chance in 200,000,000 $25,000 1 chance in 90,000,000 $5,000 1 chance in 4,000,000 $400 1 chance in 500,000 A watch valued at $90 1 chance in 4,000 (a) Find the expected value (in dollars) of the amount won by one entry. (b) Find the expected value (in dollars) if the cost of entering this sweepstakes is the cost of a postage stamp (34 cents)

Answer 1

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Answer:

a)

Prize	Chances	P(X=x)
$10,000,000	1 chance in 200,000,000	0.000000005
$350,000	1 chance in 200,000,000	0.000000005
$25,000	1 chance in 90,000,000	0.0000000111
$5,000	1 chance in 5,000,000	0.00000002
$400	1 chance in 400,000	0.0000025
A watch valued at $90	1 chance 4,000	0.00025

The expected number of the amount won by one entry is obtained as below:

E(X)	P(X=x)	E(X)*P(X)
$10,000,000	0.000000005	0.05
$350,000	0.000000005	0.00175
$25,000	0.0000000111	0.000277778
$5,000	0.00000002	0.0001
$400	0.0000025	0.001
A watch valued at $90	0.00025	0.0225
	SUM (E(X)*P(X))	0.075627778

= 0.07563

b)

The expected value if the cost of entering this sweepstakes is the cost of a postage stamp 34 cents is calculated as follows:

= 0.07563-0.34 = -0.264