I have some questions about the quiz questions:
Q1: Assume that there are 2 happy people and 2 unhappy people in a room. Concretely, persons A and B are happy and persons B and C are unhappy. If you were to randomly pick a person from the room, what is the probability that the person is happy?
In this question, B is both happy and unhappy. So, there are 3 people to pick, among them A and B are happy. Wouldn’t the probability be 2/3? But there is no such answer. Or even if we consider B as unhappy, it would be 1/3, but this answer is not available either. Is the duplication of B a mistake in the question, or there is something I’m missing?
Q5: Suppose that in your dataset, 25% of the positive tweets contain the word ‘happy’. You also know that a total of 13% of the tweets in your dataset contain the word ‘happy’, and that 40% of the total number of tweets are positive. You observe the tweet: '‘happy to learn NLP’. What is the probability that this tweet is positive?
P(happy|pos) = 0.25, P(happy) = 0.13, P(pos) = 0.4. So, P(pos|happy) = 0.25*0.4/0.13=0.7692308. But this answer is graded as wrong answer. Did I understood it wrong, or it is just the numerical precision tolerance problem?