1. A friend who works in a big city owns two cars, one small and one large.Thrce
ID: 2928470 • Letter: 1
Question
1. A friend who works in a big city owns two cars, one small and one large.Thrce quarters.f the time he drives the small car to work, and one-quarter of the time he drives the large car he takes the small car, he usually has little trouble parking, and so is at work on time probability 0.9. If he takes the large car, he is at work on time with probability 0.6. Given that with he was on time on a particular morning, what is the probability that he drove the small car? P(IS) p() 152 2, Explain what prior probability in Bayesian analysis refers to. 3 lain what posterior probability in Basiaanalsis refers to.Explanation / Answer
P(S) = 0.75
P(L) = 0.25
P(T|S) = 0.9, P(T|L) = 0.6
P(S|T) = P(T|S).P(S) / P(T)
= P(T|S).P(S) / ( P(T|S).P(S) + P(T|L).P(L)) = 0.9*0.75/(0.9*0.75 + 0.6*0.25) = 0.818
2. The prior probability is observing the probability of the event beforehand, i.e. our expectation of the event before it has occured, i.e. P(S) here
The posterior probability is the probability of observing the event given that another event has happened, i,e. P(S|T) here. i.e. probability that small car was chosen given that person reached on time
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