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### Aircraft Disappearances

```
Date: 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:

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:

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/
```
Associated Topics:
High School Probability

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