Assignment#3 Total marks: 80 Due Date: 26-03-2024 Question#1: A box contains 7 white balls and 3 red balls. Three balls are drawn at random. In how many ways can three ball be drawn if a) b) c) d) e) the color is not considered. Two balls are white and one is red All three balls are white At least one ball is white All three balls are red Question#2 How many permutation of the letters can be made from the word “COMMITTEE”? Question#3 In how many ways can an instructor select five students for a group project out of a class of 12? Question#4 In a city election there are 4 candidates for mayor,3 candidates for deputy, and 6 candidates for secretary. In how many ways can these four offices be filled? Question#5 Find the number of permutations that can be formed from all the letters of the words. a) b) c) d) PROPOSITION PRESEVERANCE DISCUSS BANANA Question#6 A candidate is contesting for both National and provincial assembly seats. The probability that he will win the national seat is 0.8 and he will win the provincial seat is 0.6. what is the probability that a) He will win both seats b) He will win at least one seat. c) He will lose both the seats. Question#7 given that event A and B are independent, and P(A)=0.3 and P(B)=0.6 Compute the following probabilities 𝑃(𝐴 ∩ 𝐵) , 𝑃(𝐴 ∪ 𝐵) , 𝑃(𝐴̅ ∪ 𝐵̅ ), 𝑃(𝐴̅ ∩ 𝐵̅ ) , 𝑃(𝐵/𝐴) Question#8 The probability that a doctor correctly diagnosis a particular illness is 0.7. Given that the doctor makes an incorrect diagnosis, the probability that the patient enters a law suit is 0.09, what is the probability that the doctor makes an incorrect diagnosis and the patient sues? Question#9 There are three families each having four children. Two boys and two girls, three boys and one girl, one boy and three girls. A child from each party is invited to a party. Find the probability that (a) only girls turn up for party (b) only boys turn up for party (c) two girls and one boy turn up for party Question#10 A bag contains four red counters and six black counters. A counter is picked at random from the bag and not replaced. A second counter is then picked. Find the probability that (a) the second counter is red given that that the first counter is red (b) both counters are red (c) the counters are of different colors. Question#11 A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1 percent of the healthy person tested. (that is, if a healthy person is tested, then, with probability 0.01, the test result will imply that he or she has the disease) if 0.5 percent of the population actually has the disease, what is the probability that a person has the disease given that test result is positive? Question 12 There are 272 employees in an organization 0.95 of them are female.an employee is selected at random, find the probability that he is male?
