Suppose a sunny day is followed by a sunny day with probability 0.7, and a cloudy day is followed by a sunny day with probability 0.5. a. if it is sunny today, what is the probability that it will be sunny 3 days later?

Establish a transition matrix:

The possible path are:

sunny -> cloudy -> cloudy -> sunny

-> sunny -> sunny

-> sunny -> cloudy -> sunny

-> sunny -> sunny

Find and add all the paths using the transition matrix T:

0.3*0.5*0.5 + 0.3*0.5*0.7 + 0.7*0.3*0.5 + 0.7*0.7*0.7 = 0.628

a. she will receive a refund of $278.

step-by-step explanation: