Aircraft DisappearancesDate: 01/29/98 at 21:15:25 From: Jenny Ko Subject: conditional probability Seventy percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 90% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. a. If it has an emergency locator, what is the probability that it will not be discovered? b. If it does not have an emergency locator, what is the probability that it will be discovered? Date: 01/29/98 at 21:46:48 From: Doctor Gary Subject: Re: conditional probability Do you know what "conditional probability" is? It's just a fancy way of saying that we already know something. Here's how it can work: If I choose an integer at random from 1 to 10 inclusive, the probability that it is 6 is one in ten, or .1. However, if I choose an EVEN integer at random within the same range of numbers, the conditional probability that it is 6 becomes one in five, or .2, because the condition that the number be even means that we don't have to consider some of the possibilities we might otherwise have to take into account. Perhaps we could understand the information in the story better if we imagined that there were 100 light aircraft that disappeared in whatever certain country the story is concerned with. Seventy of them would be recovered, and 60% of THOSE SEVENTY have an emergency locator. 60% of 70 is 42, so we can break those aircraft that disappeared and were later discovered into two groups: 42 had emergency locators 28 didn't have emergency locators. We're told that 90% of the aircraft not discovered didn't have a locator, but we have to use our memory and common sense to notice that this is 90% of THIRTY planes, or 27. We can now group the planes that weren't discovered: 3 had emergency locators 27 didn't have emergency locators >Suppose a light aircraft has disappeared? >a. If it has an emergency locator, what is the probability that it will not be discovered? Of every 100 light aircraft that disappear, 45 have emergency locators, and only 3 are not discovered. The "conditional" probability that a lost plane with an emrgency locator will not be discovered is 3/45. >b. If it does not have an emergency locator, what is the probability that it will be discovered? 55 planes that get lost don't have emergency locators. 28 are discovered. You can take it from there. -Doctor Gary, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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