Two students are asked to go to the board to work

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.

What is 6/10 rounded to the nearest half

Item 1 which question could the expression 1000n answer? let n = the number of gallons of gas used. how many miles per gallon did the car get driving 1000 miles? let n = the number of grams of food needed for each dog. how many grams of food are needed to feed 1000 dogs? let n = the number of people at the show. how many empty seats were there at the show if there are 1000 seats at the theater? let n = the number of seats at the theater. how many empty seats will there by if 1000 people come to the show?