An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny

The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Step-by-step explanation:

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this