Question

Question Write the correct values in the boxes. For this question, working is not required and will not be marked Two of many kinds of bets you can make on a horse race are ‘win, and Place. In each of these you noininate往horse, say 'Neddy', pay some money (your ‘stake') and maybe get some money back (your 'payout'). The payout, if paid, is stakexodds, where 'odds is a number greater than 1 specified by the betting agency. The odds number is different for Win and Place. You will get the payout if, and only if Win: Neddy wins the race. Place: Neddy is 'placed' in the race; ie. Neddy comes Ist, 2nd or 3rd in a race with at least eight horses, or comes st or 2nd in a race with from five to seven horses. Place bets are not allowed on races with less than five horses. Your return' or profit' on the bet is payout-stake, (and is usually negative!) At the Canberra races you fancy Neddy's chances in Race (10 horses). You estimate he has 10% chance, of winning, a 40% chance of coming in 2nd or 3rd, and, consequently, a 50% chance of being unplaxed·The bookmaker offers odds of 6.50 on a win and 2.20 on a place. Based on your estimated probabilities find the expected return on: (a) 'S10 on Neddy to win' (a Win bet with $10 stake) (b) ‘$20 on Neddy for a place, (a Place bet with S20 stake) A third kind of bet is 'Each-way'. This is just two bets on the same horse, one for a win and one for a place, with equal stakes. So for example 'S10 each way on Neddy' means 810 to win and S10 for a place and so costs you S20. Note that if the horse wins, an each-way bet pays twice; once for the win and once for the place. Basedon the same odds and probabilities as above, find the expected return on ( S10 each way on Neddy' In Race 2 (6 horses) you consider betting on Nelly at odds of Win:25.00, Place:5.00. (d) At what probability of Nelly winning would a Win bet on Nelly have an expected return of $0? (e) At what probability of Nelly being placed would a Place bet on Nelly have an expected return of 80? (f) In fact you believe Nelly has a 5% chance of winning and a 5% chance of coming 2nd At these probabilities, what is your expected return on a 810 cach-way bet on her?

Answer 1