A jar contains 5 red marbles and 8 white marbles . Event A = drawing a white marble on the first draw Event B = drav drawing a red marble on the second draw If two marbles are drawn from the jar , one after the other without replacement , what is P(AandB) expressed in simplest form? a: 3/13
b: 10/39
c: 5/12
d: 8/13

The figure shows the front side of a metal desk in the shape of a trapezoid. what is the area of this trapezoid? 10 ft²16 ft²32 ft²61 ft²

1.based of the diagrams what is the the value of x? 2.how would you verify your answer for x

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.