SOLUTION: Problems using Conditional Probability; Events Involving "AND" One Problem encountered by developers of the space shuttle program is air pollution in the area surrounding the la

Question 1001263: Problems using Conditional Probability; Events Involving "AND"
One Problem encountered by developers of the space shuttle program is air pollution in the area surrounding the launch site. A certain direction from the launch site is considered critical in terms of hydrogen chloride pollution from the exhaust cloud. It has been determined that weather conditions would cause emission cloud movement in the critical direction only 5% of time.Find the probability of each event. Assume that probabilities for a particular launch in no way depend on the probabilities for other launches. ( Give answer to two decimal places.)
41) A given launch will not result in cloud movement in the critical direction.
42) No cloud movement in the critical direction will occur during any of 5 launches.
43) Any 5 launches will result in at least one cloud movement in the critical direction.
44) Any 10 launches will result in at least one cloud movement in the critical direction.
In the book the odd answers for 41) is 0.95 and 43) is 0.23
Solutions showing work for all four would be great.Thanks.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
41. A given launch has a probability of a bad outcome of 5% and therefore a good outcome of 95%. A good outcome is not in the critical direction.
42. No cloud movement in critical direction is (0.95)^5=0.774, assuming independence.
43. At least 1 is 1- probability of 0. We already know that the probability of 0 for 5 launches is 0.774. Therefore, the probability of at least 1 is 1-0.774=0.226 or 0.23. You don't need to compute the probability of 2,3,4,5 bad outcomes for this problem.
44. Any 10 launches is the probability of 10 without subtracted from 1, as in the previous question. (0.95)^10=0.599, so the probability of at least one bad outcome is 1-0.599=0.401 or 0.40.

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