For questions #1 and #2, let A be the statement that says that it will be sunny

ID: 3005450 • Letter: F

Question

For questions #1 and #2, let A be the statement that says that it will be sunny in Columbus on March 21st.

1. (A) Suppose person M prefers the bet

(i) Get $10 if A

(ii) To get $10 if two head are flipped in a row with a fair coin.

What can you conclude about their betting rate on A?

(B)

Suppose that same person M also prefers bet

(iii) Get $10 if one head is flipped on the first flip of a fair coin.

To be (i) from (a).

What can you conclude about their betting rate on A?

Suppose person N is indifferent between bet

(i) Get 10$ if A

and

(iv) Get $5 if ~A That is, they are willing to take either bet.What can you conclude about N’s betting rate on A?

How is it related to N’s betting rate on ~A?

1 a) Stattement A can either be True orr False, each with probability half. Expected return = 1/2*10 = $5

Betting rate is therefore 5/10 or 1/2

(ii) To get 2 Heads in a row, prob = 1/2*1/2 = 1/4. Return = 10*1/4 = 2.5. Rate is 2.5/10 = 1/4

(iii) Getting Head on 1st flip has prob 1/2. Hence betting rate is 5/10 = 1/2

2 (i) Get $10 if A is exactly same as 1(i). Losing that bet would be get $10 - $5 = $5 if ~A. They are complimentary bets and the rate is same, 1/2

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