Math 245 Written Homework 3 Due April 25th Name: 1. Consider the experiment of flipping a coin (sides of the coin are \"Heads\" and \"Tails\") and rolling a 6-sided die (each side has numbers 1,2,3,4,5 or 6). (a) Give the sample space S of this experiment. (b) Determine the event B = coin is tails and die is an even number. (Die is 2,4,6) (c) Determine the event C = die is a multiple of 3. (Die says 3 or 6.) (d) Determine the event D = coin is heads. (e) Are the events from (b) and (c) mutually exclusive? What is their intersection B C? (f) Are the events from (b) and (d) mutually exclusive? What is their intersection B D? 1 2. On a given day in Oregon, the probability of rain is 60% and the probability of sun is 50%. It will rain or there will be sun for certain, with probability 100%. What is the probability it will be raining and there will be sun at the same time? 3. Of the 193 member countries of the United Nations, 54 are in the African Group, 55 are in the Asia-Pacific group, 23 are in the Eastern European group, and 33 are in the Latin American group. The rest of the countries are in the Western European and others group. (a) Write down the probability distribution for picking a UN country at random and determining its group. Group Probability African Asia-Pacific Eastern European Latin American Western European and Others (b) What is the probability that the country is in the African Group? (c) What is the probability that the country is in the Eastern European or Asia-Pacific group? (d) What is the probability a country is not in the Latin American group? 2