Let X denote the number of times Ron Weasley manages to irritate Professor Snape in one day. Then X has the following probability distribution: x f(x) 0 0.15 1 0.20 2 0.20 3 0.30 4 0.15 (a) () Find the probability that Ron will get in trouble with Professor Snape at least two times in one day. Round your answe

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?