1) A multiple-choice exam has six problems, each of which has three possible answers.

What is the probability that John will get four or more correct answers by just guessing?

2) If the number of particles emitted per second by a particular radioactive material has a Poisson distribution with mean of 10 particles, determine the following:

a. The probability of at most 3 particles in one second.

b. The probability of more than 1 particle in one second.

3) On average, 25% of the products manufactured by a certain company are found to be defective. If we select four of these products at random and denote the number of the four products that are defective by the variable X, determine the mean and variance variance of X.

4) The number of cars that arrive at gas station at an average of 50 cars per hour. The station has only one attendant, and each car requires exactly one minute to fill up. If we define a waiting line as the condition in which two or more cars are found at the same time at the gas station, what is the probability that a waiting line will occur at the station?