(Solved): Probability of Independent Events 1. A fair coin is tossed twice. Determine the probability of gett ...

Probability of Independent Events 1. A fair coin is tossed twice. Determine the probability of getting heads in both tosses. (hint draw tree diagram) 2. Two six-sided dice, A and B, are used in a game. Dice A has 3 ned sides and 3 white sides. Dice B has 4 red sides and 2 blue sides. Both the dice are thrown together. Find the probability that a. both dice have a red side facing upwards b. only a dice has a red side facing upwards 3. The probability that a patient is allergic to medicine X is 0.3. Medicine X is administered to three patients, P. Q and R. Find the probability that a. all of them are allergic to it b. only patient P is allergic to it c. two of them are allergic to it d. none of them are allergic to it 4. The probabilities that Suhaila passes his Mathematics, Science and History tests are 0.82, 0.74 and 0.69 respectively. Find the probability that Suhaila a passes her Mathematics test only b. passes two of the three tests c. fails all of the three tests. Focus on Exam 1. How many three-digit numbers can be formed from the digits 1,2,3,4,5 and 6 if a. repetition is not allowed? b. repetition is allowed? 2 The probability that candidate A will faill a certain job interview is 0.3 while the probability that candidate 8 will fail the job interview is 0.4. The probability that both A and B will fail the job interview is 0.05. What is the probability that at least one of these two candidates will fail the job interview? 3. SU Bank records that 75% of its car loans are completely repaid. Analysis on the unpaid loans shows that 85% were made to applicants who had been employed at their present jobs for less than two years. Of the repaid loans, 25% were made to applicants who had been employed at their present jobs for less than two years. a. Draw a tree diagram for the above problem b. What is the probability that a particular loan applicant would have been employed at his or her present job for less than two years? c. Given that a particular loan applicant has spent only one year on the present job, what is the probability that this person will repay the loan?