i really need help to understand this.. I can almost figure it all out but i need detailed explanation especially for question 3.. and if possible can you please send me a screenshot of the excel work so i can understand more.. thank you for your time

We assume that the probability of a passenger forgetting their luggage on the train is 0.005. A train carries 250 passengers. It will be admitted that these travelers have gathered together at random and that their behavior. in relation to their luggage, is independent of each other. We denote by X the random variable which takes as a value the number of travelers who forgot their luggage on the train. 1) What is the probability law of the random variable X? 2) Calculate its expectation and its variance. 3) Give. by iustifying the answer. a probability law making it possible to approximate the law found in the previous question. 4) Using this approximation. calculate an approximate value of the probability ot the following events: a) \"No traveler has forgotten their luggage". b) \"At least ve travelers have forgotten their luggage\". c) \"At most one traveler has forgotten their luggage\