Question

In November, the rain in a certain valley tends to fall in storms of several days duration. The unconditional probability of rain on any day of the month is 0.600. But the probability of rain on a day that follows a rainy day is 0.900, 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.​

Answer 1

Answer:

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​

Step-by-step explanation:

Rain on November 1:

0.9 of 0.6(rain on Oct 31).

0.3 of 0.4(not rain on Oct 31).

Rain on November 2:

Considering rain on November 1, 0.9 probability of rain.

Rain on November 3:

Considering rain on November 2, 0.1 probability of rain.

Find the probability of rain on November 1 and 2, but not on November 3.​

Multiplicating the probabilities:

$p = (0.9*0.6+0.3*0.4)*0.9*0.1 = 0.0594$

0.0594 = 5.94% probability of rain on November 1 and 2, but not on November 3.​