I've got a probability question:
Given a 5-faced die (1,2,3,4,5),call it die $A$, each face has probability as follows:
$\begin{array}{rrrrr} \text{Face} & 1 & 2 & 3 & 4 & 5 \\ \text{Prob} & 0.2 & 0.15 & 0.1 & 0.25 & 0.3 \end{array}$
We roll this die three times and get $O = \{2,4,5\}$
Q1. What's the probability that we get this kind of outcome assuming that we are using die A
My solution is: $3!\cdot0.15\cdot0.25\cdot0.3$,
Q2. Given another 5-faced die $B$ and its probability distribution is as follows:
$\begin{array}{rrrrr} \text{Face} & 1 & 2 & 3 & 4 & 5 \\ \text{Prob} & 0.1 & 0.2 & 0.3 & 0.25 & 0.15 \end{array}$
Now, we have 2 dice, given that we do not know which die we rolled, but the outcome is $O = \{2,4,5\}$, whats the probability this die is die A?