Question

At a raffle, 1500 tickets are sold at $2 each for four prizes of $500, $250, $150, and $75. Assume all 4 prizes are drawn at the same time (so there is no change in probability between selections of the prizes), and assume all 1500 tickets have an equal chance of being selected.

A. Create the probability model for money won from the purchase of one ticket.

B. Find and interpret the expected value for one play.

C. Find and interpret the standard deviation for one play.

D. Find the expected value and standard deviation for 3 plays.

Answer 1

A)

Probability model - The price is assumed to be won only once for a category, There are total 1500 tickets. Thus, probability of each is 1/1500.

x	500	250	150	75
p(x)	1/1500	1/1500	1/1500	1/1500

B)

Expected value = E(X) = sum(pi*xi)

= 500*1/1500 + 250*1/1500 + 150*1/1500 + 75*1/1500

= 0.65

Thus, expected value for 1 play = $0.65

C)

E(x^2) = sum(pi*xi^2)

= 500^2*1/1500 + 250^2*1/1500 + 150^2*1/1500 + 75^2*1/1500

= 227.08

std deviation = sqrt(variance)

= sqrt( E(X^2) - E(X)^2)

= sqrt(227.08 - 0.65^2)

= 15.055

Thus, standard deviation of one play is $15.055

D)

Multiplying or dividing by a constant means that the standard deviation will be multiplied or divided by the same constant

Expected value for 3 plays = 3*0.65 = $1.95

standard deviation for 3 plays = 3*15.055 = $45.165