In November the rain in a certain valley tends to fall in st

In November, the rain in a certain valley tends to fall in storms of several day\'s duration. The unconditional probability of rain on any given day of the month is 0.500. But the probability of rain on a day that follows a rainy day is 0.700, and the probability of rain on a day following a nonrainy day is 0.300. Find the probability of rain on November 1 and 2, but not on November 3. Find the probability of rain on November 1, and 2, but not on November 3 is

Solution

Probability of rain on November 1 is 0.5

Given rain on November 1 probability of rain on NOvember 2 is :0.7

Given rain on November 2 probability of no rain on November 3 is:0.3

So total probability is: 0.5*0.7*0.3=0.105