A student has to take 5 exams at the end of the module. Suppose that he will pass each of these exams with probability 0.9, independently of the other exams.

(a) What is the probability the student will pass at least 3 exams?

(b) What is the expectation and the standard deviation of the number of passed exams?

(c) The student has decided that he will buy a new iPhone 11 Pro if he passes all the exams, or buy an iPhone 11 if he fails only one exam, or buy nothing if he fails more than one exam. What are the expectation and the standard deviation of the student's expenses? Assume the price of an iPhone 11 Pro is $999 and the price of an iPhone 11 is 699$.