Douglas A. Buckler EC315 Homework #1 1) If two dice are rolled, what is the probability that the two numbers that turn up are the same? =1/6 x 1/6 = 1/36 2) If two dice are rolled, what is the probability that the two numbers that turn up are different? = 1 - 1/36 = 35/36 3) In a college with 15 faculty members and 250 students, there is to be formed a committee consisting of three faculty and five students. How many such committees are possible? = (250! x 15!) / ( (250-5)! x (15-3)!)) = 217945728000 4) Suppose a marksman has the probability of 0.3 of hitting the bull's eye. What is the probability that in 20 trials she will make: a) exactly 8 bull's eyes? = 0.12 b) no more that 3 bull's eyes? = 0.22 5) During an average day, the number of patients that seek help in the Benefis emergency room is 16. What is the probability that on any given day the number of patients that seek help will be: a) 18? = 0.21 b) 4? = 0.046 6) If one was to deal just 5 cards at a time, how many different five-card hands can be dealt from a 52-card deck? = 311875200 7) An urn contains three red, four white, and five blue balls. A second urn contains one red, six white, and three blue balls. One ball is selected at random from each urn. Find the probability that: a) The balls are the same color? = 3/12 x 1/10+4/12 x 6/10+5/12 x 3/10 = 0.35 b) One is red and one is white? = 3/12 x 6/10 + 1/10 x 3/12 = 0.175 c) Neither is blue? = 7/12 x 7/10 = 0.4083 8) Given two jars each containing 3 red, 6 blue, and 1 white marbles, if a marble is chosen at random from the first jar and placed into the second and then a marble is randomly chosen from the second jar, find the probability that the final marble is: Red ; 4/11 Blue ; 7/11 White ; 2/11 Orange. = 0 9) The voters in a large city are 40% white, 40% black, and 20% Hispanic. A black mayoral candidate anticipates attracting 30% of the white vote, 90% of the black vote, and 50% of the Hispanic vote. What percent of the overall vote does the candidate expect to get? = 26% 10) Suppose I average one flat tire every 6000 miles. I then set out on a 15,000 mile trip. What is the probability that I will have more than one flat? = 0.4