For each of these following examples, define the random variable of interest and recognize distributions respectively (one of the distributions learnt in class- Binomial, Multinomial, rgeometric, Negative Binomial, Geometric, Poisson). Do not solve the problems in this part. example, you find a r.v. X given in the question follows a binomial distribution. Then you to specify the parameters B(n =?, p =?) according to our slides. An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled? Suppose you are given a 3 question multiple-choice test. Each question has 4 responses and only one is correct. Suppose you want to find the probability that you can just guess at the answers and get 2 questions right. A crate contains 50 light bulbs of which 5 are defective and 45 are not. A Quality Control Inspector randomly samples 4 bulbs without replacement. What is the probability that 4 bulbs are defective? Let's say that 80% of all business startups in the IT industry report that they generate a profit in their first year. If a sample of 10 new IT business startups is selected, find the probability that exactly seven will generate a profit in their first year. Bob is a high school basketball player. He is a 70%% free throw shooter. That means his probability of making a free throw is 0.70. During the season, what is the probability that Bob makes his third free throw on his fifth shot? Your basketball team is playing a series of 5 games against your opponent. The winner is those who wins more games (out of 5). Let assume that your team is much more skilled and has 75% chances of winning. It means there is a 25% chance of losing. What is the probability of your team gets 3 wins? Births in a hospital occur randomly at an average rate of 1.8 births per hour. What is the probability of observing 4 births in a given hour at the hospital? Bob is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. During the season, what is the probability that Bob makes his first free throw on his fifth shot? A box of candies has many different colors in it. There is a 15% chance of getting a pink candy. What is the probability that exactly 4 candies in a box are pink out of 10? A deck of cards contains 20 cards: 6 red cards and 14 black cards. 5 cards are drawn randomly without replacement. What is the probability that exactly 4 red cards are drawn