I did a quick search, couldn't find an answer that helps me understand this question:
Supposed there is a company with a problem, they can either assign one big team C (30% chance to solve) or two smaller teams A (20% chance) and B (10% chance) to solve it. If team A solves the problem - team B has a 5% chance to solve the problem. Which team setup is better?
P(A) = 0.20, P('A) = 0.80, P(A|B) = 0.10, P('A|B) = 0.90, P(A|'B)= 0.11, P('A|'B) = 0.7888 P(B) = 0.10, P('B) = 0.90, P(B|A) = 0.05, P('B|A) = 0.95, P(B|'A)=0.1125, P('B|'A) = 0.8875
This is where I got stuck and have a few questions:
1) For simultaneous events, with conditional probability, does the sequence of events lead to different probabilities? As in does Team A succeeding first or not need to be taken into account as well as Team B - leading to total probability of solving the problem = P(B|A)P(A) + P('B|A)P(A) + P(A|B)P(B) + P('A|B)P(B)?
2) If we assume that the team that completes it first will notify the other team, how would we be able to include or combine the earlier probability in? That is if A finishes it first (P(A) = 0.20) + B finishes it first (P(B) = 0.10) + A doesn't finish it, and B does plus the opposite (P('A AND B) + P(A AND 'B))?
I think I am thinking too much into this problem... would sincerely appreciate your help as I honestly suck at probability questions and would love to learn how to conceptualize these.