Suppose that a student will be either on time or late for a particular class and

Question

Suppose that a student will be either on time or late for a particular class and that the events that he is on time or late for the class on successive days form a Markov chain with stationary transition probabilities. Suppose also that if he is late on a given day, then the probability that he will be on time the next day is 0.8. Furthermore, if he is on time on a given day, then the probability that he will be late the next day is 0.5.

If the student is on time a given day, what is the probability that he will be late on eah of the next three days?

Explanation / Answer

Solution- Let us denote the following events -

A: Student is on time B: Student is late

then P(B|A) = P( student is late given that he was on time the previous day) = 0.5

and P(A|A) =  P( student is late given that he was late the previous day) = 1-0.8 = 0.2

Now require probability =  P(B|A) * P(A|A) * P(A|A)

= .5 * .2 * .2

= 0.02

Answer

TY!

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