# Thread: Matrix - transition problem2

1. ## Matrix - transition problem2

If Regan passes his math test, the probability that he will pass the next one is 97%. If he fails his math test, the probability that he will pss the next one is only 85%
Regan has worked hard on this unit so the probability that he will pass the first test is 95%

a) Write the initial and the transition matrix
b) What's the probability that Regan will pass the fifth test?

The transition matrix would be
0.97 0.03
0.85 0.15

the initial one...

2. ## Re: Matrix - transition problem2

Hi,
yes ur transition matrix is correct.
He will pass the first test,the intial probability distribution is given by A(0)=[1,0].
The probability that regan will pass the fifth test is=A(0)p^4 [i.e if u take transition matix is p then find p^4 matrix]
next u find the matix mltiplication for A(0) and p^4 u get the required result.

3. ## Re: Matrix - transition problem2

Regan has worked hard on this unit so the probability that he will pass the first test is 95%

the initial shouldn't be [0.95,0.95]?

4. ## Re: Matrix - transition problem2

Originally Posted by deepashree
Hi,
yes ur transition matrix is correct.
He will pass the first test,the intial probability distribution is given by A(0)=[1,0].
The probability that regan will pass the fifth test is=A(0)p^4 [i.e if u take transition matix is p then find p^4 matrix]
next u find the matix mltiplication for A(0) and p^4 u get the required result.
No, the initial vector should be A(1) (not A(0) since the transition matrix only applies after he has taken a test) equal to [.95, .05]. And, since that is the probability vector for the first test, the probability that he will pass the first 5 tests is the first component of $\displaystyle p^4A(1)$ (or $\displaystyle A(1)p^4$ depending upon your notation) where p is the transition matrix.

5. ## Re: Matrix - transition problem2

Thanks,
Great explanations

"In mathematics you don't understand things. You just get used to them." Johann von Neumann