Applied Management Statistics - Homework 4 1. A single 6-sided die is rolled. What is the probability of rolling a 4 or a 1? 2. There are 12 balls in a hat, 4 of them are red, and 8 of them are blue. 2 of the red ones and 3 of the blue ones are signed by a marker. What is the probability of taking a red, signed ball? 3. In a farm, there are 20 white sheeps (16 white and 4 black ones) and 8 horses (3 white ones and 4 black ones). If we choose an animal randomly, what is the probability that it is a black sheep? And that it is a white horse? In how many different ways can we choose 5 white sheeps and 2 black horses? 4. A number from 0 to 999 is chosen at random. What is the probability of choosing a number between 100 and 199 or an even number? 5. If we know that in a city A, 31% of the men wear hats, 52% of the population is women and in total 45% of the population wears hat, what is the probability that a randomly chosen person is a man or wearing a hat? 6. In a village 10% of the population earns 1200, 25% of them earns 1500, 55% of them earns 1900 and the rest is unemployed (no income), what is the expected salary if we choose a person randomly? 7. Assume that in a group of 100 people, 40 does not have any child, 30 people have 1 child, 20 people have 2 children, 5 have 3 children, 3 have 4 children and 2 have 5 children. If we randomly choose a person, what is the expected number of children he/she has? 8. We have an investment opportunity with following possible outcomes: 10% of probability that we lose 40, 40% probability that we earn 80 and 50% probability that we earn 50. What is the expected profit/lost