Question

Seventy percent of 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 an emergency locator. Suppose that 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?
c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is
the probability that 7 of them are discovered?

Answer 1

Part a

Therefore, the probability that it will not be discovered given that it has an emergency locator is 0.067.

Part b

Therefore, the probability that it will be discovered given that it does not have an emergency locator is 0.509.

Part c

The probability that 7 of them are discovered is 0.215.

Explanation:

(a)

Define the events to find the probabilities.

Let

Locator

Discovered

And,

No Locator

Not discovered

The known probabilities are,

P(D)=0.7

P(D) =1-P(D)

= 1-0.7

= 0.3

P(LD)=0.6

P(L|D)=1-P(LD)

=1-0.6

= 0.4

P(L|D) =0.9

P(L|D)=1-P(L|D)

=1-0.9

= 0.1

Also,

P(DOL)=P(L|D)P(D)

= (0.7)(0.6)

= 0.42

P(DO L) = P(L|D)P(D)

= (0.4)(0.7)

= 0.28

P(DOL)= P(L|D)P(D)

= (0.1)(0.3)

= 0.03

P(Dn L) = P(L|D)P(D)

= (0.9)(0.3)

= 0.27

And,

P(L)=P(DOL)+P(DOL)

= 0.42+0.03

= 0.45

P(L) =1-P(L)

= 1-0.45

= 0.55

The probability that it will not be discovered given that it has an emergency locator is,

P(DL)- P(DOL)

P(L)

0.03

0.45

= 0.067

Part a

Therefore, the probability that it will not be discovered given that it has an emergency locator is 0.067.

Explanation | Hint for next step

Using the definition of a conditional probability, the probability that it will not be discovered given that it has an emergency locator is 0.067.

Step 2 of 3

(b)

The probability that it will be discovered given that it does not have an emergency locator is,

P(D|L) - P(DOL)

P(L)

0.03

0.55

= 0.509

Part b

Therefore, the probability that it will be discovered given that it does not have an emergency locator is 0.509.

Explanation | Hint for next step

Using the definition of a conditional probability, the probability that it will be discovered given that it does not have an emergency locator is 0.509.

Step 3 of 3

(c)

Let X be the number of aircrafts discovered.

Given that of the aircraft that are discovered, 60% have an emergency locator

Let the probability of success bep=0.60

.

The probability that 7 of them are discovered is,

P(X= 7+(19)10.00*(1-0.60)

= 0.215

Part c

The probability that 7 of them are discovered is 0.215.

Explanation

Using the binomial probability law, the probability that 7 of them are discovered is 0.