When there are few data, we often fall back on personal probability. there had been just 24 space shuttle launches, all successful, before the challenger disaster in january 1986. the shuttle program management thought the chances of such a failure were only 1 in 100,000. suppose 1 in 100,000 is a correct estimate of the chance of such a failure. if a shuttle was launched every day, about how many failures would one expect in 300 years? [a] (round to the nearest integer.)

The rows and columns of lattice points in a three-by-three square array are evenly spaced one unit apart. how many distinct triangles with at least one side of length 2 units can be drawn using three lattice points for the vertices?

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.

The frequency table shows the results of a survey asking people how many hours they spend online per week. on a piece of paper, draw a histogram to represent the data. then determine which answer choice matches the histogram you drew. in order here is the.. hours online: 0-3, 4-7, 8-11, 12-15, and 16-19. frequency: 5, 8, 10, 8, 7 answer for the question is in the picture! : )