Imagine that you’re in a game show and your host shows you three doors. Behind one of them is a shiny car and behind the others are goats. You pick one of the doors and get what lies within. After making your choice, your host chooses to open one of the other two doors, which inevitably reveals a goat. He then asks you if you want to stick with your original pick, or switch to the other remaining door. What do you do? Most people think that it doesn’t make a difference and they tend to stick with their first pick. With two doors left, you should have a 50% chance of selecting the one with the car. If you agree, then you have just fallen afoul of one of the most infamous mathematical problems – the Monty Hall Problem. In reality, you should switch every time which doubles your odds of getting the car. Over the years, the problem has ensnared countless people, but not, it seems, pigeons. The humble pigeon can learn with practice the best tactic for the Monty Hall Problem, switching from their initial choice almost every time. Amazingly, humans do not!
Which of the following conclusions follow from the passage above?
Which of the following conclusions follow from the passage above?
Show Hint
- Humans calculate the probability of independent, random events such as the opening of a door by dividing the specific outcomes by the total number of possible outcomes.
- Humans find it very difficult to learn to account for the host’s hand in making the event non-random and, thereby, changing the outcome of the event.
- Calculating probabilities is difficult for humans but easy for pigeons; which is why the pigeons succeed where the humans fail.
- Humans are governed by reason, but pigeons are irrational and only interested in the outcome and will do whatever it takes to get food.
The Correct Option is A, B
Solution and Explanation
Step 1: Evaluate each option.
- (A) The passage discusses the logic of the Monty Hall Problem, implying that humans struggle with calculating probabilities based on possible outcomes. This conclusion follows directly from the passage.
- (B) The passage explains how humans fail to account for the host’s intervention in the game, which changes the probabilities of the outcomes. This conclusion also follows from the passage.
- (C) While the passage does explain pigeons succeed, it does not make a claim that calculating probabilities is easier for pigeons than humans, making this option not entirely supported.
- (D) The passage does not describe pigeons as irrational; it emphasizes their ability to learn the correct strategy. This option does not follow from the passage.
Step 2: Conclusion.
Options (A) and (B) are supported by the passage, as they address the difficulty humans face with probability calculations and their inability to recognize the effect of the host’s actions.
Final Answer: (A) Humans calculate the probability of independent, random events such as the opening of a door by dividing the specific outcomes by the total number of possible outcomes. (B) Humans find it very difficult to learn to account for the host’s hand in making the event non-random and, thereby, changing the outcome of the event.
Top Questions on Probability
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
- Two dice (one red and one blue) are thrown. Find the probability that the sum is prime and the number on the red die is greater than the blue die.
- If there are two red and blue dice. Find the probability when the sum of the dice is a prime number, where the number on red is more than blue.
- Two dice are thrown. Defined are the following two events A and B: \[ A = \{(x, y) : x + y = 9\}, \quad B = \{(x, y) : x \neq 3\}, \] where \( (x, y) \) denote a point in the sample space. Check if events \( A \) and \( B \) are independent or mutually exclusive.
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
Questions Asked in GATE XH-C1 exam
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:
Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.
Abuse \( \rightarrow \) Insult \( \rightarrow \) Ridicule
__________ \( \rightarrow \) Praise \( \rightarrow \) Appreciate
- Had I learnt acting as a child, I ________ a famous film star.
Select the most appropriate option to complete the above sentence. - A car started from city P at 9:40 AM. The time taken for the car to reach city Q is 4 hours and 50 minutes. The time of arrival of the car at city Q is: