The probability of rain on any particular day is 0.2. However, the probability of rain on a day after a rainy day is 0.85, whereas the probability of rain on a day after a non-rainy day is 0.1 . Question in details (below)?
On three consecutive days, find the probability of having three rainy days.
On three consecutive days, find the probability of having three rainy days.
2 Answers
It is 14.45 percent
Explanation:
The first day is independent from the day before. Therefore the first day probability (of rain) is 20 percent.
The second day (depends on the previous day) rainfall probability is 85 percent.
Finally, the third day (it must be rainy to satisfy the total probability) rainfall probability is 85 percent.
The probability of having three consecutive days which are rainy:
P(all rainy)
or 14.45 percent.
The probability of having
Explanation:
This is a regular Markov Chain.
The initial matrix is
The transition matrix is
Therefore,
The probability of having
The infinite matrix is
such that
We have
Also,
and
Therefore,