Canned fishare sold in bulk from the wholesale .They are packaged in boxes with different dimensions as shown below Thabong Secondary school intends to buy canned fish for the National School Nutrition Programme Canned fish diameter =76mm height=10cm. Box A length=36cm Breadth=25cm height=35cm .Box B length=50cm Breadth=20cm height=35cm (a)the number of cans that can fit along the lengths of the boxes (b) the number of cans needed along the width of the boxes (c)the number of cans that can fit on the bases of the boxes

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.