section 6.1 homework\nscore: 11.28/21 answered: 11/21\nquestion 15\nthe ohio lottery has a game called pick…

section 6.1 homework\nscore: 11.28/21 answered: 11/21\nquestion 15\nthe ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the four numbers come up in the order you picked, then you win $2100.\na) write the probability distribution for a players winnings.\nfill in the table below.\nfor the computer to grade this one correctly make sure that your x values are from smallest to largest.\nx\np(x)\nb) what are your expected winnings?\nround final answer to 2 decimal places. put correct units in the second box.

section 6.1 homework\nscore: 11.28/21 answered: 11/21\nquestion 15\nthe ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the four numbers come up in the order you picked, then you win $2100.\na) write the probability distribution for a players winnings.\nfill in the table below.\nfor the computer to grade this one correctly make sure that your x values are from smallest to largest.\nx\np(x)\nb) what are your expected winnings?\nround final answer to 2 decimal places. put correct units in the second box.

Answer

Explanation:

Step1: Determine the number of possible outcomes

The total number of four - digit numbers is (10\times10\times10\times10=10000) (since each digit can be one of 0 - 9).

Step2: Calculate the probability of winning

The probability of winning (P(X = 2100)) is (\frac{1}{10000}=0.0001), and the probability of losing (P(X=- 1)) is (1 - \frac{1}{10000}=\frac{9999}{10000}=0.9999). So the probability distribution table:

(X) (P(X))
(-1) (0.9999)
(2100) (0.0001)

Step3: Calculate the expected value

The formula for the expected value (E(X)=\sum xP(x)). So (E(X)=(-1)\times0.9999 + 2100\times0.0001=-0.9999+0.21=- 0.7899\approx - 0.79)

Answer:

(X) (P(X))
(-1) (0.9999)
(2100) (0.0001)
The expected winnings are (-0.79)