Question

the 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. a) write the probability distribution for a players winnings. fill in the table below. for the computer to grade this one correctly make sure that your x values are from smallest to largest.

x	p(x)
- 1	0.9999
2100	0.0001

score on last try: 0.71 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorrect part. jump to last submitted part. next question. get a similar question. you can retry this question below.

Explanation:

Step1: Define the random - variable

Let \(X\) be the player's winnings. The player pays \(1\) dollar to play. If they win, they get \(2100\) dollars in net (since they paid \(1\) dollar initially), so \(X = 2100\) with a certain probability, and if they lose, \(X=- 1\) (losing the \(1\) - dollar bet).

Step2: Determine the probabilities

The probability of winning is the probability of picking the correct four - digit number. There are \(10\times10\times10\times10 = 10000\) possible four - digit numbers (since each digit can be one of 10 values from 0 to 9). So the probability of winning \(P(X = 2100)=\frac{1}{10000}=0.0001\). The probability of losing \(P(X=-1)=1 - \frac{1}{10000}=0.9999\).
The probability distribution table is:

\(X\)	\(P(X)\)
\(2100\)	\(0.0001\)

Answer:

\(X\)	\(P(X)\)
\(2100\)	\(0.0001\)