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.
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) |