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