Question

The Ohio lottery has a game called Pick 4 where a player pays $2 and picks a four-digit number. If the four numbers come up in the order you picked, then you win $1500. What is your expected value? Round to the nearest cent, if necessary. The expected value is $

Answer 1

Number possible four-digit numbers (0000 to 9999) : 10000

Number of possible four numbers come up in the order you picked = 1

Therefore Probability of winning $1500 = 1/10000= 0.0001

Cost to pay the game = $2

Net value = $1500 - $2 = $1498

X : Net value

P(X=$1498) = 0.0001

Probability of not winning = 1 - Probability of winning $1500 = 1-0.0001 = 0.9999

Cost to play the game =$2

Net value = -$2

P(X =-$2) = 0.9999

Therefore Probability distribution of X

x	P(x)
1498	0.0001
-2	0.9999

Expected Value = E(X)

Expected value = $-1.85

The expected value is $-1.85