While navigating the deep waters of possibility, sometimes even the simplest problems can wreak havoc on our brains. This delicate mathematical dance often challenges our intuition and often leads us to unexpected results.
For example, the classic two-door problem… It seems like a simple choice game, right? But the underlying math sometimes challenges even the sharpest minds. So you? Now you are faced with 5 different probability questions that make you think and turn your predictions upside down…
Note: We have a surprise in this content. After reading all the content, we will explain what this surprise is in the bottom paragraph.
1) A bag contains 5 balls in total, 2 blue and 3 red balls. If we randomly draw 2 balls from the bag, what is the probability that both balls are blue?
Let’s take some time for the answer.
If you’re ready, let’s get right to the answer.
- The probability of drawing a blue ball in the first step is 2/5 because there are a total of 5 balls and 2 of them are blue.
- In the second step, there are now 4 balls in the bag and one of them is blue. So the probability of drawing the second blue ball is 1/4.
- The probability of both events occurring is found by multiplying these two probabilities. So (2/5) * (1/4) = 2/20 = 1/10. So the probability of both balls being blue is 10%.
2) Three people enter a room and sit on a chair at random. What is the probability that these three people will sit in the same chair when they leave the room and re-enter, sitting in randomly chosen chairs?
Let’s take some time for the answer.
If you’re ready, let’s get right to the answer.
- In this question, in order for three people to sit in the same chair, each person must sit in the first chair they sit in. In this case, the probability of each person randomly choosing the chair they will sit on is 1/3 because there are 3 different chair choices for each person.
- Therefore, the probability that these three people will sit in the same chair will be (1/3) * (1/3) * (1/3) = 1/27. So the probability of these three people sitting in the same chair is 3.70%.
3) People living in a village either always tell the truth or always lie. Liars and truth tellers are indistinguishable.
You came to this village and found two people: Ali and Ayşe. Ali said, “Ayşe is a liar.” said. Ayşe said, “We are both the same type.” said. How do you know if Ali and Ayşe are telling the truth or a liar?
Let’s take some time for the answer.
If you’re ready, let’s get right to the answer.
- To understand this situation, we have to look at what Ayşe said. If Ayşe is telling the truth, it means that Ali is also telling the truth because Ayşe said “We are both the same type”. However, in this case, Ali’s statement “Ayşe is a liar” creates a contradiction because we accept that Ayşe is telling the truth.
- If Ayşe is a liar, then Ali’s statement “Ayşe is a liar” is true. However, Ayşe’s statement “We are the same type” would be a lie, in which case we would assume that Ali and Ayşe are of different types, which means that Ali is telling the truth. Therefore, Ayşe is a liar and Ali is a truth-teller.
4) You enter a room and there are two doors inside. Behind one door is freedom, behind the other is death.
There are two guards guarding the gates, one of whom always tells the truth and the other always lies. But you do not know which watchman is telling the truth and which guard is lying. You have to choose the right door to exit the room, and for that you can only ask one question to a guard. What question would you ask?
Let’s take some time for the answer.
If you’re ready, let’s get right to the answer.
- I asked one of the two guards, “If I asked the guard next to you which door is the door to freedom, what would he say?” you may ask.
- When you ask this question, you encounter two situations:
- If you have chosen the truth-telling watchman, that lying watchman knows that he will lie and shows you the door that leads to death.
- If you choose the lying watchman, he knows that the other guard will tell the truth, but because he lied, he will again show you the door that leads to death.
- In both cases, the door the watchman shows you leads to death. Therefore, you reach freedom by choosing the other door that is not shown to you.
Would you like the continuation of such probabilistic questions, which are close to each other but are enjoyable to solve? So let’s move on to our surprise. All of the questions and answers in this content were produced by artificial intelligence. So, would you like to answer similar logic questions from artificial intelligence? Come on comment!
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