Yay.

How to tackle 5-stem True/False questions with negative marking within each question?

It would appear as if guessing confers no advantage as each correct guess (50% chance) would be negated by an incorrect one (50% chance). However, negative marking occurs only within each question, i.e deductions do not spill over to other questions. This creates a statistical advantage, especially so when there’s lots of guessing to do.

Let's try to work it out.

Scenario 1: Unsure of 1 stem, i.e. can answer 4 stems

Do not answer. Outcome: 4 marks
Guess 1 stem. Outcome: 3 marks 50%, 5 marks 50%. E(x) = 4

Recommendation: No difference in E(x). Go with your gut.

Scenario 2: Unsure of 2 stems

Do not Answer - 3 marks
Guess 1 - 2 marks 50%, 4 marks 50%. E(x) = 3
Guess 2 - 1 mark 25%, 3 marks 50%, 5 marks 25%. E(x) = 3

Recommendation: No difference in E(x). Guess 2 "feels" safe enough with a 75% safety margin (improvement or no change), though it makes no difference statistically. Again a matter of gut feeling.

Scenario 3: Unsure of 3 stems

Do not Answer - 2 marks
Guess 1 - 1 mark 50%, 3 marks 50%. E(x) = 2
Guess 2 - 0 mark 25%, 2 marks 50%, 4 marks 25%. E(x) = 2
Guess 3 - 0 mark 12.5%, 1 mark 37.5%, 3 marks 37.5%, 5 marks, 12.5%. E(x) = 2.125

Recommendation: Guess 3 for the favourable E(x).

Scenario 4: Unsure of 4 stems

Do not Answer - 1 mark
Guess 1 - 0 mark 50%, 2 marks 50%. E(x) = 1
Guess 2 - 0 mark 25%, 1 mark 50%, 3 marks 25%. E(x) = 1.25
Guess 3 - 0 mark 50%, 2 marks 37.5%, 4 marks 12.5%. E(x) = 1.25
Guess 4 - 0 mark 31.25%, 1 mark 37.5%, 3 marks 25%, 5 marks 6.25%. E(x) = 1.4375

Recommendation: Guess 4 for the best E(x).

Scenario 5: Unsure of all 5 stems

Do not Answer - 0 mark
Guess 1 - 0 mark 50%, 1 mark 50%. E(x) = 0.5
Guess 2 - 0 mark 75%, 2 marks 25%. E(x) = 0.5

Guess 3 - 0 mark 50%, 1 mark 37.5%, 3 marks 12.5%. E(x) = 0.75

Guess 4 - 0 mark 68.75%, 2 marks 25%, 4 marks 6.25%. E(x) = 0.75
Guess 5 - 0 mark 50%, 1 mark 31.25%, 3 marks 15.625%, 5 marks 3.125%. E(x) = 0.9375

Recommendation: Go all the way for the best E(x).

Interesting point to note: By guessing all 125 stems, the expected score is 23.4375 upon 125, which equates to an 18.75% score for this CA.