p.286. no 10.- Two hundred draws will be made at random with replacement from the box -3, -2, -1, 0, 1, 2, 3 (a) If the sum of the 200 numbers drawn is 30, what is their average? (b) If the sum of the 200 numbers drawn is –20, what is their average? (c) In general, how can you figure the average of the 200 draws, if you are told their sum? (d) There are two alternatives: (i) Winning $1 if the sum of the 200 numbers drawn is between –5 and +5 6 Winning $1 if the average of the 200 numbers drawn is between –0.025 and +0.025.
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Your friend, in his/her moves, can split the board only horizontally and can retain either the lower or the upper half. After two moves by each player a single cell will remain which can no longer be split and the number in that cell will be treated as the gain (in rupees) of the person who has started the game. A sample game is shown below. 2 1 2 4 2 1 2 1 1 5 1 6 7
The clearest examples of individual’s choice between uncertain options are provided by gambling and insurance. An individual who purchases home insurance is accepting the certain loss of a small premium in preference to the combination of a small chance of a much larger loss (fire, theft etc) and a large chance of no loss. He pays a premium to avoid risk as he prefers certainty to uncertainty, he is risk averse. An individual who purchases a lottery ticket is subjecting himself to a large chance of losing a small amount (£1 for lottery ticket) and a small chance of winning a large amount, rather than keeping his £1 to avoid risk all together (Friedman, Savage. 1948).
Representations: If you want to win the game, you should start with an even number. If you want you to lose or get your opponent to lose, start with an odd number. You want to have an odd number land in your spot because the final result to win is odd (1). An odd number can only have odd divisors, so when you subtract it by an odd it will become and even and you will lose. So, to win you must start with an even number.
7) Find the sum of three whole numbers is 7 X , 2x=1, ( 6-3x) (6-3x)+x=(2x+1)-3 6-2x=2x-2 8=4x X=2. The three numbers are 5,2, and 0 since the only other two numbers that can be used to equal 7 would be 5 and 0 8) Eggs + Meats must be ≤ 300Mg 150e+ 100m ≤ 300 9) See attached graph file 10) See attached graph
Problem 3. A country uses as currency coins with values of 1 peso, 2 pesos, 5 pesos, 10 pesos and bills with values of 5 pesos, 10 pesos, 20 pesos, 50 pesos, and 100 pesos. Find a recurrence relation for the number of ways bn to pay a bill of n pesos (for n ≥ 101) if the order in which the coins and bills are paid matters. SOLUTION: We break bn up according to which coin or bill was used first. If we start with a 1 peso coin, then there are bn−1 ways to finish paying the bill.
That’s $.15 per quart of profit that the company will be losing due to Margaret’s decision. However, had Margaret shared all of the information with the company’s controller, and they had agreed that it would mutually beneficial to continue paying her friend $.75 per quart, though the market price is $.60 per quart, then it would a the controller’s decision and it would be a completely informed decision. As a freight broker, I have had
Result, everyone was picking the number 44! Sunk cost bias: another possible explanation of the gambler’s fallacy. Playing a game costs money, we expect something in return sooner or later. Having made that initial investment and not had a return we feel obliged to continue so we don’t lose out. Long term we could potentially lose a lot
The White family was warn by Sergeant Major Morris, but they ignored him and wish for 200 pounds. Herbert White son says “why we’re going to be rich, and famous and happy, Wish to be an emperor, Father to begin with; then you can’t be bossed around” (49). However, even before Sergeant Major Morris gave it to the White family, he said “I threw it on the fire if you keep it, don’t blame me for what happens” (48). He also tells them “The first man had three wishes, yes” was the reply; “I don’t know what the first two were, but the third was for death” (48). Even with life threating situation, the Whites greed and want for money is more important that their own