i) What gives the greater probability of hitting some target at least once: A: h
ID: 3301193 • Letter: I
Question
i) What gives the greater probability of hitting some target at least once: A: hitting in a shot with probability 1/2 and firing 1 shot, or B: hitting in a shot with probability 1/3 and firing 2 shots? First guess. Then calculate. ii) An Auckland based laboratory employs 600 engineers and other researchers. The laboratory operates, among other tools and equipments, facilities that include a concrete testing laboratory and 12 quake simulators. Before deciding whether to purchase new equipment, the director would like to know how many members regularly use each facility. A survey of the employees indicates that 70% regularly use the concrete testing laboratory, 50% regularly use the quake simulators, and 5% use neither of these facilities regularly. (a) Find the probability that a randomly selected employee uses the quake simulator or the concrete testing laboratory regularly. (b) Find the probability that a randomly selected employee uses the quake simulator and the concrete testing laboratory regularly. (c) Given that a randomly selected employee uses the quake simulator regularly, find the probability that they also use the concrete testing laboratory regularly.Explanation / Answer
Question 4:
i) A) Here clearly the probability of hitting the shot is 0.5
B) Here we have 2 shots, each having a hit probability of 1/3
Therefore probability that atleast one of the hit hits is computed as
= 1 - Probability that both misses
= 1 - (2/3)2
= 5/9 = 0.5556
Therefore B is a higher probability of hitting the target
ii) Here we are given that:
P( concrete testing laboratory ) = 0.7, P( quake simulators ) = 0.5 and
P( neither of the 2 facilities ) = 0.05
a) Probability that the employee uses the quake simulator or the concrete testing laboratory
= 1 - P(neither of the 2 facilities )
= 1 - 0.05
= 0.95
Therefore 0.95 is the required probability here.
b) Probability that they use both can be computed as:
P( concrete testing laboratory or quake simulators ) = P( concrete testing laboratory ) + P( quake simulators ) - P( concrete testing laboratory and quake simulators )
Therefore,
P( concrete testing laboratory and quake simulators ) = P( concrete testing laboratory ) + P( quake simulators ) - P( concrete testing laboratory or quake simulators ) = 0.7 + 0.5 - 0.95 = 0.25
Therefore 0.25 is the required probability here.
c) Given that the emplyee uses the quake simulator, probability that they also use the concrete testing lab is computed using Bayes theorem as:
P( concrete testing laboratory | quake simulators ) = P( concrete testing laboratory and quake simulators ) / P( quake simulators )
P( concrete testing laboratory | quake simulators ) = 0.25 / 0.5 = 0.5
Therefore 0.5 is the required probability here.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.