1. An adversary of the West has a factory that builds nuclear bombs in violation
ID: 3175925 • Letter: 1
Question
1. An adversary of the West has a factory that builds nuclear bombs in violation of anagreement with the North Atlantic Treaty Organization. The factory is protected by a systemof S-300 surface-to-air missiles.
The French military base in Erbil, the capital of the Republic of Kurdistan, has 30 fighter jets:20 Lockheed F-35s and 10 Mitsubishi F-3s. Each aircraft has exactly one SPEAR air-to-surface missile.
President Marine Le Pen has ordered a squadron of 5 jet fighters – three F-35s and two F-3s– to depart from Erbil. They will fly to the location of the factory and fire their SPEAR missilesat it.
The location at which the SPEAR missile impacts the ground can be modeled by a normaldistribution. The mean of the distribution is the exact location of the factory. The mean is 0
kilometer, and the standard deviation is 2 kilometers.
The probability that an F-35 avoids being shot down by an S-300 missile before firing theSPEAR missile is 0.10 . The probability that an F-3 avoids being shot down by an S-300
missile before firing the SPEAR missile is 0.15 .
The operation of each fighter jet and each SPEAR missile is independent of the operation ofthe other fighter jets and the other SPEAR missiles.
a. Calculate the number of ways of selecting a squadron of three F-35s and two F-3s fromthe 30 aircraft that are parked at the military base.
b. Calculate the probability that, at least, one aircraft in the squadron avoids being shot downby an S-300 missile before firing the SPEAR missile.
c. The factory will be obliterated if and only if, at least, one SPEAR missile impacts theground within 0.5 kilometer of the factory. Calculate the probability that the factory will be
obliterated.
Explanation / Answer
A) Number of ways in which three F-35d and two F-3s can be selected form the squadron = 20C3 x 10C2
= 51300
B) The probability of at least one aircraft avoids being shot down = 1-P(all aircrafts being shot down)
= 1 - (1-0.1)3x(1-0.15)2
= 1 -0.5267
= 0.4733
C) P(missile impact within 0.5km)
Z= (X-mean)/standard deviation = 0.5/2 = 0.25
P(missile impact within 0.5km) = P(Z=0.25) - P(Z=-0.25)
= 0.5987-0.4013
= 0.1974
P(factory will be obliterated) = 0.1974
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