This is the question problem i have in my tutorial sheet in school. It is about pairwise independent and mutually independent
Generally, i have listened to my lecturer explaining how those two are different but i still can not get out of the confusion and can’t really understand or how to differentiate between those two.
The problem below has very short answer. Just two calculation, but i do not know how they arrive to that answer. Specifically, for every pair of color, we have the probability is .25. But if it is pairwise between 3 colors(?), it is still .25 ( i don’t get this point) and that is different from mutually between 3 colors which is .125. And the problem is solved!
Events $A_1,...,A_n$ are (mutually) independent if for any $m$ indices $1 ≤ i_1 < i_2 < ··· < i_m ≤ n$, $P(\bigcap_jA_i) = P(A_i)$ .
Consider a regular tetrahedron (a polyhedron with 4 identical triangular face with one face painted green, one red, one blue and another one which is painted with all 3 colors. The tetrahedron is rolled and we note the face it lands on. Let $G, R,$ and $B$ be the events that the face has green, red and blue respectively. Show that these events are pairwise independent but not (mutually) independent.
Please help me explaining that question
Thank you so much :)