Question

section 6.1 homework
score: 11.28/21 answered: 11/21
question 15
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)
b) what are your expected winnings?
round final answer to 2 decimal places. put correct units in the second box.

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:

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

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:

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

The expected winnings are \(-0.79\)