Seventy percent of the light aircraft that disappear while in flight in a certai

Question

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 an aircraft has disappeared.

Consider the two events D: The disappeared aircraft is discovered, and L: the disappeared aircraft has a locator.

a. What is the probability that a disappeared aircraft will have a locator?

b. If it has an emergency locator, what is the probability that it will not be discovered?

c. Are the events being discovered and having a locator independent?

Explanation / Answer

Sorry, by mistake, I read seventy as seventy eight. Here is the revised solution.

(a) 42% or 0.42

(b) 3/30 = 0.10

(c) No, because P(L | D) P(L)

Locator No locator Total Discovered 60% of 70 = 42 70 - 42 = 28 70 Not discovered 30 - 27 = 3 90% of 30 = 27 30 Total 45 55 100

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