Consider a situation in which p(x) = 4/5 and p(y) = 1/4. if p(x and y) is = 1/5, which best describes the events?
they are independent because p(x) x p(y) = p(x and y).
they are independent because p(x) + p(y) = p(x and y).
they are dependent because p(x) x p(y) = p(x and y).
they are dependent because p(x) + p(y) = p(x and y).

This question awards 100 ! i really don’t want to fail i will also mark you !

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?

Simplify (1/2)4th power a. (1/16) b.(1/8) c.(1/4)