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Elizan Lecnnor ©w3Aamoez Week 7 In class Worksheet : EXPECTED VALUE A probability distribution chart is used to quickly show various events and their probabilities. The events are called random variables and are labeled x. 1) At Tucson Raceway Park, your horse, Chester has a probability of 1/20 of coming in first place, a probability of 1/10 of coming in second place, and a probability of 1/4 of coming in third place. First place pays $4,500 to the winner, second place $3,500 and third place $1,500. We want to know if it is worthwhile to enter the race if it costs $1,000 to enter. To do this, we need to know what our expected return is. Notice that in this problem, x is your winnings, or how much money you walk away with. a) If you win the first prize what is your net return? Remember that you need to pay $1000 to enter the race. %,SO() b) What is the net return if you win the second prize? 2,500 ¢) What is your net return for the third prize? S0 d) What if you do not win a prize? What is your net return then? — | OO e) What is the probability of not winning? Remember that the total probability is always 1. (4 e S @I ¢ (© % éf OtD ;?{D?,.\\;\\\‘*fi\q, f) Use all of the above information to complete the probability distribution table below. Remember that x is your winnings, not the advertised prize. 1stPlace |2"Place |3" Place ' Losing S ’ -—\0""7 { xl RS5° 150 AR | G g) What is the expected net return? | < / ¢ SIS s X gn + L5eAp hSMé, S ,50 + N S | Wie, 0t h) Do you think it is worthwhile to enter the race? ol
Week 7 In class Worksheet : EXPECTED VALUE 2) You decide to enter a contest where you pay $5 for a chance at the spinner. If you s and if you spin an odd number, you will win $10. What are your expected winnings? (Make sure you create the probability distribution table first) Pin a 0, you will win $100 . 0. | @m S /‘MV\‘)‘I\'\{/\&. | *W“MY\VKWT*@T\‘«' R
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