A school requires students to wear uniforms. if a student randomly selects one item from each of the following categories, then what is the probability they will be wearing all navy with the following items? 2 cardigans one grey, one navy. 4 polos one white, one navy, one maroon, one black. 2 bottoms one khaki, one navy?

Which of the following circles have their centers in the third quadrant? check all that apply.

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.

Bo is buying a board game that usually costs bb dollars. the game is on sale, and the price has been reduced by 18\%18%. which of the following expressions could represent how much bo pays for the game? choose 2 answers: choose 2 answers: (choice a) a 0.82b0.82b (choice b) b 1.18b1.18b (choice c) c b-0.18b−0.18 (choice d) d b-18b−18 (choice e) e b-0.18bb−0.18b