4 a two students james a and james b are both registered for a certain

Question

4. (a) Two students, James A and James B, are both registered for a certain course.Assume that James A attends 80% of the time, and James B attends 60% of the time, and the absences of the two students are independent. i. What is the probability that at least one of the two students will be in class on a given day? ii. If at least one of the two students is in class on a given day, what is the probability that James A is in class that day? (b) Two fair six-sided dice are thrown. If their total score is 7, they are thrown once more.What is the probability the final total score outcome is odd? (c) Assume that a calculator has a 'random number' key and that when the key is pressed an integer between 0 and 99 inclusive is generated at random, all numbers being equally likely and generated independently of one another. i. Let X denote the random number generated when the key is pressed once. Write down the probability function of X. (2 marks)ii. If two numbers are generated, what is the probability that the first number exceeds the second number?(4 marks) iii. If five numbers are generated, what is the probability that at least one number occurs more than once?