As a prize, you have been given the chance to pick a free ticket for one of three

lotteries. Suppose your utility u of money m is given by u (m) = V(m - 10).

According to the principle of maximizing expected utility, you should pick a free ticket for which lottery?

Lottery 1| winnings

Lottery 2 winnings

Lottery 3 winnings

Decision matrix

probability probability = probability =

= 0.5

0.4

0.1

$74

$131

526

$110

$91

$35

$26

$26

$131

To determine which lottery ticket you should choose according to the principle of maximizing expected utility, we need to calculate the expected utility for each lottery. The utility function provided is $ u(m) = \sqrt{m - 10} $.

Here are the winnings and their probabilities for each lottery:

**Lottery 1:**
- Probability = 0.5, Winnings = $74
- Probability = 0.4, Winnings = $131
- Probability = 0.1, Winnings = $26

**Lottery 2:**
- Probability = 0.5, Winnings = $110
- Probability = 0.4, Winnings = $91
- Probability = 0.1, Winnings = $26

**Lottery 3:**
- Probability = 0.5, Winnings = $35
- Probability = 0.4, Winnings = $26
- Probability = 0.1, Winnings = $131

We'll calculate the expected utility for each lottery.

### Lottery 1
For each possible winning amount, calculate $ u(m) $:
- $ u(74) = \sqrt{74 - 10} = \sqrt{64} = 8 $
- $ u(131) = \sqrt{131 - 10} = \sqrt{121} = 11 $
- $ u(26) = \sqrt{26 - 10} = \sqrt{16} = 4 $

The expected utility $ EU $ for Lottery 1 is:
\[
EU_1 = (0.5 \times 8) + (0.4 \times 11) + (0.1 \times 4) = 4 + 4.4 + 0.4 = 8.8
\]

### Lottery 2
- $ u(110) = \sqrt{110 - 10} = \sqrt{100} = 10 $
- $ u(91) = \sqrt{91 - 10} = \sqrt{81} = 9 $
- $ u(26) = \sqrt{26 - 10} = \sqrt{16} = 4 $

The expected utility $ EU $ for Lottery 2 is:
\[
EU_2 = (0.5 \times 10) + (0.4 \times 9) + (0.1 \times 4) = 5 + 3.6 + 0.4 = 9
\]

### Lottery 3
- $ u(35) = \sqrt{35 - 10} = \sqrt{25} = 5 $
- $ u(26) = \sqrt{26 - 10} = \sqrt{16} = 4 $
- $ u(131) = \sqrt{131 - 10} = \sqrt{121} = 11 $

The expected utility $ EU $ for Lottery 3 is:
\[
EU_3 = (0.5 \times 5) + (0.4 \times 4) + (0.1 \times

Learn how to maximize expected utility when choosing a lottery ticket among three options. Calculate the expected utility using the given utility function and probabilities for each lottery. Suitable for advanced learners interested in decision theory and probability calculations.

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