Question

Question 6 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 nominate a 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 1st, 2nd or 3rd in a race with at least eight horses, or comes 1st 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 1 (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 unplaced. 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) $10 on Neddy to win (a Win bet with $10 stake). (b) $20 on Neddy for a place (a Place bet with $20 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 $10 each way on Neddy' means $10 to win and $10 for a place and so costs you $20. Note that if the horse wins, an each-way bet pays twice; once for the win and once for the place. Based on the same odds and probabilities as above, find the expected return on (c) "$10 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 $0? (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 $10 each-way bet on her?

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