TOP GUN EXERCISE STAT5100 7) The landing of military fighter jets on aircraft ca
ID: 3020430 • Letter: T
Question
TOP GUN EXERCISE
STAT5100
7) The landing of military fighter jets on aircraft carrier requires great skill , so on occasions it requires more than one attempt to achieve the landing. TOP GUN is a pilot who is assigned to an aircraft carrier and has a record of achieving 94 % of landings on aircraft carriers in the first attempt. In a particular exercise TOP GUN is assigned to make three (3) takeoffs and landings on the aircraft carrier to which it is assigned. Under the assumption that the resulting events in each landing attempt are statistically independent of each other determine:
a) The probability that TOP GUN achieve three (3) landings in the first (1) try.
b) The probability that TOP GUN achieve at least one (1) landing out of the three (3) on the first try.
c) The probability that TOP GUN fails to perform any of the three (3) landings in the first try.
Explanation / Answer
n = 3
probability of landing at 1st = 0.94
probability not landing at 1st = 1-0.94 = 0.06
a) all 3 at 1st try = 3C3*(0.94)^3*(0.06)^0 = 0.830
B) ATLEAST 1 LANDING AT 1ST TRY = 1 - 0 LANDING AT 1ST TRY
THEREFORE PROBABILITY THAT ALL 3 LANDS NOT IN 1ST TRY = 3C0*(0.94)^0*(0.06)^3 = 0.0002
HENCE PROBABILITY OF AT LEAST 1 = 1 - 0.0002 = 0.9998
C) PROBABILITY THAT ALL 3 LANDS NOT IN 1ST TRY = 3C0*(0.94)^0*(0.06)^3 = 0.0002
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