To the right is a diagram of a prize wheel. When Dave spins the wheel, he is awa

Question

To the right is a diagram of a prize wheel. When Dave spins the wheel, he is awarded the amount on the wheel indicated by the pointer. If the wheel points to Bankrupt, he loses the total amount he has accumulated and also loses his turn. Assume that the wheel stops on a position at random and that each position is equally likely to occur. a) Determine Dave's expectation when he spins the wheel at the start of the game (he has no money to lose if he lands on Bankrupt). b) If Dave presently has a balance of $1700, determine his expectation when he spins the wheel. a) Dave's expectation at the start of the game is (Round to the nearest cent as needed.) b) Dave's expectation with $1700 is $ (Round to the nearest cent as needed.)

Explanation / Answer

a) as there are 12 partitions; each partition has probability =1/12

therefore expectation =(1/12)*(100+200+300+400+500+600+700+800+900+1000)=5500/12=$458.33

b)as he has $1700 and probability of going bankrupt or losing those =1/12

therefore expectation =(1/12)*(100+200+300+400+500+600+700+800+900+1000-1700)=316.67

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