Exercise 8. McDonald's Happy Meals are child-sized burger meals that come with a toy. Assume that the toy is randomly chosen from among 5 options. I already have 2 toys. (a) What is the probability that my next happy meal comes with a toy that I don't already have? (b) What is the probability that I will have to buy 3 happy meals before I get a toy I don't already have? Explain briefly the probability distribution function that you use to answer this question. (c) What is the expected number of happy meals I will need to buy to get all 5 toys (Hint: you may assume it is the expected number I will need to buy to get a 3rd toy, plus the expected number I then need to buy to get the fourth toy, plus the expected number I need to buy to get the fifth toy).

Calculate the probability P(E). The Heavy Weather Service predicts that for tomorrow there is a 60% chance of tornadoes, a 20% chance of a monsoon, and a 5% chance of both. What is the probability that we will be lucky tomorrow and encounter neither tornadoes nor a monsoon? P(E)

In economics, of all new products put on the market, 60% failed and are taken off the market within 2 years. Suppose a store introduces 80 new products. What is the probability that within 2 years 55 or more will fail?

You ask a neighbor to water a sickly plant while you are on vacation. Without water, the plant will die with a probability of 0.9. With water, it will die with a probability of 0.55. You are 86 % certain the neighbor will remember to water the plant.When you are on vacation, find the probability that the plant will die.Answer: You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?Answer: