A poll taken in Massachusetts in October 2012 showed Obama leading Romney by 60% to 40% in the U.S. presidential race. Let's assume that these numbers represent probabilities. I wished to make a bet with my friend on who would win Massachusetts, and we agreed to base our bet on that poll. I predicted a victory for Obama and would win a profit of $5 if I were right. Assuming we wished this to be a fair game, how much should I have agreed to pay my friend if he was right and Massachusetts went to Romney?

Roulette: You bet on numbers 1-18. What's the likelihood of winning after one trial? Explain your answer.

James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel.   -if the ball lands in a red space, he wins $25 on his 'red' but loses $5  on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000   let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23   u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053   FILL IN THE BLANK   if you play 2500 times, and Let, x (x bar)= the mean winnings (or…

Your company is considering offering 800 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 300 managers, 400 factory workers, and 800 miscellaneous staff, find the following probabilities, leaving the answers as formulas. (a) All the managers will be offered the opportunity. C     ,     C     ,     (b) You will be offered the opportunity.   C     ,     C     ,

A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers(red), as well as 0 and 00 (which are green). You bet 5 dollars that the outcome is anodd number. If you win you get 10 dollars; otherwise you lose your 5 dollars. Note:assume the 0 and 00 numbers are considered even numbers What is your expected winnings? Which of these options is best: bet on an odd number or don’t bet? Why?