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)=\frac{4}{9}\text{ ; P(B)=}\frac{2}{9}\text{ ; P(C)=}\frac{\text{2}}{9}\text{ ; P(D)=}\frac{1}{9}$$\text{Expected value of spinning the wheel once=}\Sigma(x_i\times P_{}(x_i))$$\text{Expected value of spinning the wheel once=}(\frac{4}{9}\times100)+(\frac{2}{9}\times300)+(\frac{2}{9}\times400)+(\frac{1}{9}\times800)$$\text{Expected value of spinning the wheel once=}\frac{400+600+800+800}{9}$$\text{Expected value of spinning the wheel once=}\frac{2600}{9}$$\text{Expected value of spinning the wheel once=}288.89$