I am having issues getting my head around an urn problem.
I have seven urns. First three urns contain 4 balls (1 red, 3 blue) and the last 4 urns contain 3 balls (1 red, 2 blue).
If picking totally randomly one ball from each urn. What are the odds of
- picking all red balls
- picking all blue balls
What I thought would be the correct way to calculate the all red balls was
0.25 x 0.25 x 0.25 x 0.33 x 0.33 x 0.33 x 0.33
but that answer seems wrong.
I've been trying to find a solution or explanation online but so far have not been able to. Does anyone know of any good resource to learn this from or can explain it a bit better please.
You have 7 independent experiments, i.e. $P(A_1 \cap A_2) = P(A_1)P(A_2)$, where $A_1, A_2$ are two experiments (i.e. two different urns), so you can multiply probabilities of success for each experiment.