Problema Solution
if melinda buys two tickets at the spring fling since there is a $1000 prize, one $500 prize, and five $100 prizes. there were a total of 1000 tickets sold at $3 each. what is melinda's expectation
Answer provided by our tutors
To compute the expected value, we need to find the sum of the products of the probability of each event and the amount won or lost if that event occurs:
P(winning $1000 price) = 2/1000 = 1/500
In this case Melinda will get 1000 - 2*3 = $994 (we subtract the cost of the 2 tickets)
P(winning $500 price) = 2/1000 = 1/500
In this case Melinda will get 500 - 2*3 = $594 (we subtract the cost of the 2 tickets)
P(winning $100 price) = (2*5)/1000 = 1/100
In this case Melinda will get 100 - 2*3 = 994 (we subtract the cost of the 2 tickets)
P(not winning anything) = 1 - (1/500 + 1/500 + 1/100) = 493/500
In this case Melinda will lose 2*3 = $6 (he cost of the 2 tickets)
Expected Value = (1000 - 2*3)*P(winning $1000 price) + (500 - 2*3)*P(winning $500 price) + (100 - 2*3)P(winning $100 price) + (-6)P(not winning anything)
Expected Value = 994*(1/500) + 494*(1/500) + 94*(1/100) - 6*(493/500)
Expected Value = -2
Melinda's expectation is that she will lose $2.