Question

Bill is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 thru 6. The spinner stops on a number slice at random. This game is this: Bill spins the spinner once. He wins $1 if the spinner stops on the number2, $4 if the spinner stops on the number 2, $7 if the spinner stops on the number3, and$10 if the spinner stops on 4. He loses $11 if the spinner stop on 5 or 6.

Answer 1

Given:

Bill is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 thru 6. The spinner stops on a number slice at random. This game is this: Bill spins the spinner once. He wins $1 if the spinner stops on the number2, $4 if the spinner stops on the number 2, $7 if the spinner stops on the number3, and$10

Required:

To calculate probability

Step-by-step explanation:

(a)

first we want to find the expected value in one spin:

number 1 : wins $1

number 2: wins $4

number 3 : wins $7

number4 : wins $10

number5: looses $11

number 6 : looses $11

The expected value can be calculated as:

`\begin{gathered} Ev=\Sigma X_np_n \\ where\text{ X}_n\text{ is the event and p}_{n\text{ is the probability}}_{\text{ }} \end{gathered}`

We know that the probability for all the events is 1/6 so we have:

Ev =($1+$4+$7+$10-$11-$11)*(1/6)

=$0

So the expected value for the game is $0

(b) Bill neither gain money nor looses

Required answer:

(a) $0

(b) option C