Homework Answers
Given that when it rains one day, probability for the rain the next day is 0.3 and when it does not rain on one day and probability of rain the next day is 0.03.
Let A be the state when it rains and A' be the state when it does not rain.
A) Transition diagram
From the given information,
when it rains one day, probability of rain the next day is 0.3, so probability of no rain next day is 1-0.3 = 0.7
when it does not rain on one day and probability of rain the next day is 0.03, so probability of no rain the next day is
1-0.03=0.97
The transition diagram would be:
B) Transtion matrix:
C) If it rains on thursday, the probability that the restaurant will be closed on saturday:
There are two possibities that it doesn't rain on Saturday -
Probability( It rains on thursday, it rains on Friday and it does not rain on saturday OR It rains on thursday, it does not rain on friday and it does not rain on saturday )
= 0.3x0.7 + 0.7x0.97
= 0.889
If it rains on thursday, the probability that the restaurant will be closed on Sunday:
Probability( Rains on Thursday, rains on friday, rains on saturday, does not rain on Sunday OR Rains on Thursday, rains on friday, does not rain on saturday, does not rain on Sunday OR Rains on Thursday, does not rain on friday, does not rain on saturday, does not rain on Sunday OR Rains on Thursday, does not rain on friday, rains on saturday, does not rain on Sunday )
= 0.3x0.3x0.7 + 0.3x0.7x0.97 + 0.7x0.97x0.97 + 0.7x0.03x.0.7
= 0.94
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