Final Exam: Probability and StatisticsTime: 90 minutesFull Name:Student ID:1. (4 points) Two fair six-sided dice are thrown and the numbers obtained are noted. EventS is “The sum of the numbers is even”. Event T is “The sum of the numbers is either lessthan 6 or a multiple of 4 or both”. Determine whether the events S and T are independent.2. (4 points) Alice travels to work by bicycle 70% of the time and by scooter 30% of the time.If she uses her bicycle she is late 3% of the time but if she uses her scooter she is late only2% of the time.1. Draw a fully labeled tree diagram to illustrate this situation.2. Find the probability that Alice is late for work on any particular day.3. (4 points) The probability density function ofX, the lifetime of a certain type of electronicdevice (measured in hours), is given byfX(x) =10/x2x >100x≤10a. FindP(X >20)?b. What is the probability that of 6 such types of devices at least 3 will function for atleast 20 hours?