Step-by-step explanation: If we denote the percentage of light aircraft subsequently discovered, and the percentage of which is 70, by the mark <em>P(discovered) = 0.7</em>. Further, if the percentage of those light aircraft that are discovered and have a locator is 60, that is, <em>P(discovered / locator) = 0.6</em>, then the percentage of light aircraft that are not discovered will be <em>P(discovered ' ) = 1 - 0.7 = 0.3</em>. As is the percentage of undiscovered aircraft that do not have a locator <em>P(discovered ' / locator ') = 0.9</em>.
What we need to do is determine the probability that the missing aircraft will not be found and has a locator. So, <em>P(discovered ' / locator) = ?</em>
We will do this as follows. First of all the total percentage of aircraft discovered and having a locator is 0.7 x 0.6 = 0.42. Further, the total percentage of aircraft not discovered and lacking a locator is 0.9 x 0.3 = 0.27. Then the total percentage of aircraft discovered and lacking a locator will be 0.7 - 0.42 = 0.28. Like the total percentage of aircraft not discovered that have a locator is 0.3 - 0.27 = 0.03.
To make all this more obvious, we will show in the table
Locator Locator '
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Discovered 0.42 = 0.7 x 0.6 0.28 0.70
Discovered ' 0.03 0.27 = 0.9 x 0.3 0.30
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0.45 0.55 1.00
Then what we're looking for is the probability that the aircraft will not be discovered and has a locator will be:
P = (discovered ' / locator) = P (discovered ' / locator) / P (locator), that is
P = (discovered ' / locator) = 0.03 / 0.45 = 0.06667
