Keisha's teacher gives her the following information: • m, n, p, and q are all integers and p = 0 and q +0
A = and B =
What conclusion can Keisha make?
A+B=
mp+ng
PO
so the sum of two rational numbers is a rational number.
A+B=mpung
so the sum of a rational number and an irrational number is an irrational number.
PA
A B
mp+7g
PG
so the product of two rational numbers is a rational number.
А - В
mpng
PA
so the product of two irrational numbers is an irrational number.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.