The state of Ohio has several statewide lottery options (www.ohiolottery.com). O

Question

The state of Ohio has several statewide lottery options (www.ohiolottery.com). One of the simpler ones is a "Pick 3" game in which you pick one of the 1000 three-digit numbers between 000 and 999. The lottery selects a three-digit number at random. With a bet of $1, you win $550 if your number is selected and nothing ($0) otherwise. The Florida lottery has the same game (called CASH 3, with the STRAIGHT play option) and the same winnings structure. (a) With a single $1 bet, what is the probability that you win $550? (b) Let X denote your winnings for a $1 bet, so x = $0 or x = $550. Construct the probability distribution for X. X PX) $0 $550 (c) The mean of the distribution equals , corresponding to an expected return ofcents for the dollar paid to play

Explanation / Answer

Solution :

a) As it is gven that we choose one of the three digit number from 000 to 999.

So here total number of outcomes = 1000 and select one,so favorable outcomes = 1

Using definition of probability, Probability = Favorable outcomes/Total outcomes

So probability of you win $550 = 1/1000

b) from the part a, for x= 550 ,p =1/1000 = 0.001

So for x =0, probability = 1-0.001 = 0.999

0.001

c) the mean of distribution = (0*0.999)+(550*0.001) = 0.55

And to find expected return ,with $1 bet if you win, you will get $549 and if you lose ,you will get -$1

So expected return = (-1*0.999)+(549*0.001) = -0.45

x p(x) 0 0.999 550

0.001

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