In a state's Pick 3 lottery game, you pay $1.43 to select a sequence of three digits (from 0 to 9), such as 600. If you select the same sequence of three digits that are drawn, you win and collect $337.06. Complete parts (a) through (e).

a. how many different selections are possible?
b. what is the probability of winning?
c. if you win what is your net profit?
d. find the expected value (please show work for this part)

(01.02 lc) angle abc has point e on ray ba and point d on ray bc. points e and d are equidistant from point b. to bisect angle abc, which of the following needs to be identified for the construction? the distance between points e and d the point in the angle that is equidistant from points e and d the endpoint of rays ba and bc the point outside of the angle that is equidistant from points e and d

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.

Use the equation and type the ordered-pairs. y = 2 ^x