V 1.4.7 Assess whether the probabilities of the events (i) increase, decr ease,
ID: 3124707 • Letter: V
Question
V 1.4.7 Assess whether the probabilities of the events (i) increase, decr ease, or remai n unchanged when they are conditioned on the events (ii). (a) (i) It rains tomorrow, (ii) it is raining today (b) (i) A lottery b) )A lottery winner has black hair, (i) the lottery winner has brown eyes (c) () A lottery winner has black hair, (ii) the lottery 1.4.1 winner owns a red car. (d) (i) A lottery winner is more than 50 years old, (i) the lottery winner is more than 30 years old. Suppose that births are equally likely to be on any day. What is the probability that somebody chosen at random has a birthday on the first day of a month? How does this probability change conditional on the knowledge that the. person's birthday is in March? In February? 1.4.8 1. 1.4.9 Consider again Figure 1.24 and the battery lifetimes Calculate the probabilities: (a) A type I battery lasts longest conditional on it not failing first (b) A type 1 battery lasts longest conditional on a type battery failing first (c) A type 1 battery lasts longest conditional on a type battery lasting the longest (d) A type 1 battery lasts longest conditional on a type battery not failing first 4.10 Consider again Figure 1.25 and the two assembly lines. Calculate the probabilities: (a) Both lines are at full capacity conditional on neither 3 line being shut downExplanation / Answer
1.4.9
a)
P(I longest|I not failing first) = (0.39+0.03)/(0.24+0.39+0.16+0.03) = 0.512195122 [ANSWER]
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b)
P(I longest|II fail first) = 0.39/(0.24+0.39) = 0.619047619 [ANSWER]
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c)
P(I longest|II longest) = 0 [ANSWER]
If II is given to be longest, then it is impossible that I is longest.
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D)
P(I longest|II not failing first) = 0.03/(0.11+0.07+0.16+0.03) = 0.081081081 [ANSWER]
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