Question:
You are deciding whether to purchase a lottery ticket that costs 10 dollars and would pay out 115 dollars. What would the probability of winning have to be for the expected value of your purchase to $0?
Can someone guide me thru this question
Your expectation from is the probability probability of winning times the amount that you win. In this case, that's $$105p+(1-p)(-10)$$ There are two possible outcomes: you win the lottery and net $105$ (probability $p$)or you don't win and you are out the purchase price (probability $1-p$).
Now set the expectation equal to $0$ and solve for $p$.