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GATE 2021 XH2 – Question 24

Reasoning and Comprehension · Analytical and Logical Reasoning: Understanding relationships in statements or short passages and drawing reasonable conclusions and inferences; thinking critically to evaluate or predict an argument, identify the main and supporting arguments and predict outcomes · 2 marks · Multiple select

In the Monty Hall game, one of three doors hides a car and two hide goats. After a contestant chooses, an informed host always opens another door showing a goat and offers a switch. Many people regard the remaining doors as equally likely and keep their first choice. Switching actually doubles the chance of winning; pigeons learn this strategy with practice, while humans often do not. Which conclusions follow from this account?

  1. Humans use a favourable-outcomes divided by total-outcomes model for events they treat as independent and random.
  2. Humans find it difficult to account for the host’s intervention making the reveal nonrandom.
  3. Probability calculation is difficult for humans but easy for pigeons.
  4. Humans are rational whereas pigeons are irrational and do anything for food.

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Correct answer: (A) Humans use a favourable-outcomes divided by total-outcomes model for events they treat as independent and random.; (B) Humans find it difficult to account for the host’s intervention making the reveal nonrandom.

Explanation

The initial choice wins with probability1/3. Switching wins when the first choice was wrong, probability2/3, because the informed host removes a goat rather than a random door. The account’s human equal-odds response reflects A’s counting heuristic and B’s failure to include the host’s selection rule. Pigeons learning a successful tactic does not prove they calculate probabilities, and D is unsupported. Select A and B as the passage’s intended conclusions.

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