Lets say, few independent events are happening. $E_1, E_2,...,E_n$. The probability of each of these events happening is given as $P_1,P_2,...,P_n$. Each of these events carry weightage, say $W_1,W_2,...,W_n$ respectively. I tried building a tree like the one shown here . But its highly inefficient, for even small value of n, eg: $200$, the number of leaf nodes will be $2^{200}$.
Now, how can I find the probability of getting at least weight $W$?
Example:
Probabilities = [0.2, 0.8]
Weights = [3, 5]It means that, for the first event, there are 20% chances for that to happen. If it happens, the weightage will become 3, 0 otherwise. In the second case, there are 80% chances for that to happen. If it happens, the weightage will become 5, 0 otherwise.
Now if I want to find the probability of getting atleast Weight 4 would be like this
0.2 * 0.8 = 0.16 -> Total weight 8 (1)
0.8 * 0.8 = 0.64 -> Total weight 5 (2)
0.2 * 0.2 = 0.04 -> Total weight 3 (3)
0.8 * 0.2 = 0.16 -> Total weight 0 (4)So, the total probability of getting atleast 4 weight is 0.16 (From (1)) + 0.64 (From (2)) = 0.80
EDIT2:
The sum of all the probabilities $P_i$ need not be 1 always
$\endgroup$ 6 Reset to default
