Question

A lottery offers one $1000 prize, one $400 prize, and 10 $100 prizes. One thousand tickets are sold at $2 each. Find the expectation (expected value) if a person buys one ticket.(The answer will be in dollars, but just type the amount, not the dollar sign. Be sure to indicate whether it is positive or negative.)

Answer 1

Total number of tickets is one thousand.

Formula for probability is given below as,

`\text{Prob}=\frac{required\text{ outcome}}{total\text{ outcome}}`

Probability of one $1000 prize is given below as,

`P(\text{\$1000)=}(1)/(1000)`

Probability of one $400 prize is given below as,

`P(\text{\$400)=}(1)/(1000)`

Probability of ten $100 prize is given below as,

`P(\text{\$100)=}(10)/(1000)=(1)/(100)`

For the expected value if each person buys one ticket,

`\begin{gathered} Expected\text{ value=}((1)/(1000)*1000)+((1)/(1000)*1000)+((1)/(100)*1000) \\ \text{Expected value=}(1+1+10)=\text{\$12} \end{gathered}`

Expected value is $12