Question

In a board game, players take turns spinning a wheel with 4 spaces and values of$100, $300, $400, $800. The probability of landing on $100 is 4-9. Theprobability of landing on $300 is 2/9. The probability of landing on $400 is 2/9.The probability of landing on $800 is 1/9. What is the expected value of spinningthe wheel once?

Answer 1

Given:

Spinning a wheel with 4 spaces and values of $100, $300, $400, $800

Let A, B ,C and D be the spaces of the values of $100, $300, $400, $800.

`P(A)=(4)/(9)\text{ ; P(B)=}(2)/(9)\text{ ; P(C)=}\frac{\text{2}}{9}\text{ ; P(D)=}(1)/(9)`
`\text{Expected value of spinning the wheel once=}\Sigma(x_i* P_{}(x_i))`
`\text{Expected value of spinning the wheel once=}((4)/(9)*100)+((2)/(9)*300)+((2)/(9)*400)+((1)/(9)*800)`
`\text{Expected value of spinning the wheel once=}(400+600+800+800)/(9)`
`\text{Expected value of spinning the wheel once=}(2600)/(9)`
`\text{Expected value of spinning the wheel once=}288.89`