Question

The probability that it rains in London an any particular day is 0.2.

If it rains then the probability of it raining the following day increases to 0.35.
Consider the next two days.
What is the probability it rains on both days?

Answer 1

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)

=

0.20

×

0.85

×

0.85

=

0.1445

or 14.45 percent.