1. A box contains 10 white and 15 black marbles. Let X denotes the number of marbles selected until the first white marble is selected at random. Find E(X) and Var(X) (find numerical value)
2. A baker put 500 raisins into dough, mixed well, and made 100 cookies. You take a random cookie. What is the probability of finding at least 3 raisins in it? (find numerical value)
3. According to police sources, a car with a certain protection system will be recovered 90% of the time. If 12 of these stolen cars are randomly selected, find the probability that at least 1 car will be recovered. (find numerical value)
4. The probability that an airplane engine will fail in flight is 0.001. A two-engines airplane can fly with one engine and a four-engines airplane needs at least 3 engines to fly. Assuming that engine failures are independent of each other, which airplane is safer to fly the two-engine airplane or the four-engine airplane?