P(boy if favorite activity is swimming)
0.47
p(girl if favorite activity is sports)
0.26
p(girl if favorite activity is reading)
0.67
p(boy if favorite activity is sports)
0.74
p(favorite activity is swimming if a girl)
p(favorite activity is reading if a boy)
p(favorite activity is swimming if a boy)
p(favorite activity is reading if a girl)

The table shows the number of students who signed up for different after school activities. activity students cooking 9 chess 4 photography 8 robotics 11 select the true statements about the information in the table.

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.

Typically a point in a three dimensional cartesian coordinate system is represented by which of the following answers in the picture !