Let us consider following problem :
One thousand tickets are sold at $\$1$ each for a color television valued at $\$350$. What is the expected value of the gain if you purchase one ticket?
I would like to describe my basic problem related to this task. English is not my native language therefore I did not understand logic of statement. What I know is that we had $1000$ tickets that are sold at $\$1$ each. This means that the total revenue from $1000$ tickets is $\$1000$. Is this correct? We have a color television that costs $\$350$.
My question is:
What is the expected value of the gain if you purchase one ticket, really I don't understand the connection of purchase=buy. If I bought one ticket that cost $\$1$, and if I bought a television which costs $\$350$, then my gain will be $\$349$ correct? If I lost, then my gain will be $\$-1$ because I paid this $\$1$. What about their probability? If the probability that out of $\$1000$ I will win is $0.001$, then the probability that I will loose is $0.999$, so expected value will be
$$349\times 0.001+(-1)\times 0.999=-0.65$$
But still I do not understand logically this statement, could you describe please in a simple manner this problem?
Best Answer
A lottery is implied.
You pay $\$1$.
You win $\$350$ with probability $\dfrac1{1000}$ (your chance to have drawn the winning ticket).
So "on average", you get $\$0.35$ worth of television and your expected loss is indeed $\$0.65$.