Odds. In Exercise, answer the given questions that involve odds.
Texas Pick 3 In the Texas Pick 3 lottery, you can bet $1 by selecting the exact order of three digits between 0 and 9 inclusive, so the probability of winning is 1>1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.
a. Find the actual odds against winning.
b. Find the payoff odds.
c. The Web site www.txlottery.org indicates “Odds 1:1000” for this bet. Is that description accurate?
Let A is the event of winning. So the actual odds against winning is
Here andso actual odds against winning is
Therefore, the actual odds against winning is
Since the amount of bet is $1 and net profit is $499. So the payoff odds is
Therefore, the payoff odds are
The description ‘odds’ is not accurate. The right description is: odds against winning are 999:1 and odds against not winning are 1:999.