Question

One of the games at the carnival was Spin the Pointer, which uses a spinner like the one pictured here. A carnival ticket that costs $1.00 is required to play the game. For each $1.00 ticket, a player spins the pointer once and receives the amount of money indicated in the sector where the pointer lands on the wheel. The spinner has an equal probability of landing in each of the 8 sectors.

a. Let X represent the profit for the player from one play of the game. Complete the table below for the probability distribution of X.

X -$1.00 $0.00 $4.00
P(X)

b. Find the expected value of the profit for the player from one play of the game. You may handwrite your calculations.

Answer 1

(a)

`\begin{array}{cccc}{X} & {-\$1.00} & {\$0.00} & {\$4.00} \ \\ {P(X)} & {0.75} & {0.125} & {0.125} & \ \end{array}`

(b)

`E(x) = -\$0.25`

Explanation:

Given

See attachment for spinner

Solving (a): Complete the table

The amount paid is: $1

From the attached image, we have:

$0 = 6; $1 = 1; $5 = 1

To get the profit, we subtract $1 from the possible outcomes of the spinner.

So, we have:

-$1.00 = 6; $0.00 = 1; $4.00 = 1

The probability of each is then calculated as:

`P(-\$1.00) = (6)/(8) = 0.75`

`P(-\$0.00) = (1)/(8) = 0.12`

`P(-\$4.00) = (1)/(8) = 0.12`

So, the complete table is:

`\begin{array}{cccc}{X} & {-\$1.00} & {\$0.00} & {\$4.00} \ \\ {P(X)} & {0.75} & {0.125} & {0.125} & \ \end{array}`

Solving (b): The expected profit E(x)

This is calculated as:

`E(x) = \sum x * P(x)`

`E(x) = -1.00 * 0.75 + 0.00 * 0.125 + 4 * 0.125`

`E(x) = -\$0.25`