Probability of θ-Ω-θ-Ω-θ Sequence

[Institutions]

Given three characters that have a specific probability assigned to each of them:
Ω: .2
θ: .3
β: .4

What is the probability of having, say a sequence of 6 of these characters where the first and last character is a θ?

 

[Bacle2]

First of all: I'm not crazy, Institutions! :)

Secondly, this is a sort-of rote matter of constructing all sequences:

θ_ _ _ _ θ

and then figuring out the probabilities for all of the sequences of this type. I can't

think of a shortcut.

 

[Institutions]

First of all: I'm not crazy, Institutions! :)

Secondly, this is a sort-of rote matter of constructing all sequences:

θ_ _ _ _ θ

and then figuring out the probabilities for all of the sequences of this type. I can't

think of a shortcut.

glad you got the reference! But not so glad I have to construct a tree to solve this problem...

 

[Bacle2]

There may be an alternative: find the probability that neither the first , nor the last

elements is a θ, so you find the probability of having one of the 4 sequences:

β_ _ _ _β , β_ _ _ _Ω , Ω _ _ _ _β , Ω _ _ _ _Ω , or maybe less , depending if you

consider the order does not matter, and then the 2nd and 3rd sequences are the same.

 

[Institutions]

is it possible then that the answer is (0.3)^2 because the letters in the middle do not really matter? This is just me guessing but if the stuff in the middle doesn't matter then we can simply treat the whole problem as if it were a sequence of two?

 

[Institutions]

Oh and I made a mistake..those probabilities should add up to 1.

 

[Bacle2]

Actually, my bad; I was assuming every event had the same probability. I really

can't see any option other than considering all the cases separately. Sorry.

 

[awkward]

The probability of the sequence is simply (p(\theta))^2.

 

[Bacle2]

Ouch, I think I misread the problem. Sorry.; let me read it again more

carefully.