Resolving Probabilities of Exactly One and At Least One: Suppose the US Transportation Security Administration (TSA) requires 10% of all airplane passengers be randomly selected for a full screening before boarding a plane. Now, suppose you will travel on a plane 8 times in the coming year. (a) What is the probability that you will get screened exactly once?
(b) What is the probability that you will get screened at least once?
(c) Is the probability in favor (> 50%) of you getting screened exactly once? Is the probability in favor (> 50%) of you getting screened at least once?

Student price tickets to a movie are $1 and non student tickets are $2. 350 tickets are sold and the total amount made is $450. how many non student tickets were sold ? a) 100 b) 150 c) 200 d)250

The measures of the legs of a right triangle are 15m and 20m . what is the length of the hypotenuse

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.