I’m working through a conditional independence exercise and getting stuck on the probability calculations. In the problem I’m looking at, there’s a calculation for P13 that should result in values <0.31, 0.69> but I can’t figure out how they got there. When I try to compute it myself using the formula 0.2(0.04+0.16+0.16) for one of the columns, I get 0.072 instead of 0.31. I’m confused about how the distribution works in this case. Can someone walk me through the steps to get the correct probability values? I feel like I’m missing something fundamental about how conditional probabilities are calculated when dealing with independence assumptions. Any help would be really appreciated since I’ve been stuck on this for hours now.
This isn’t a straightforward probability calculation - you need to recognize the conditional independence structure. I’ve hit similar problems before, and the key is figuring out which variables you’re conditioning on and getting the factorization right. Your 0.072 looks like a joint probability, but P13 usually means P(X1, X3 | evidence). With conditional independence problems, you’ll want to use the independence assumption to simplify the joint distribution, then normalize. The <0.31, 0.69> result shows you’ve got a properly normalized binary outcome. Double-check you’re applying the conditional independence relationships correctly - sometimes variables only become independent after you condition on specific evidence, which totally changes how you factor the joint probabilities.
You’re calculating marginal probabilities instead of conditional ones. P13 should be a conditional probability distribution given some evidence, not a basic marginal calculation. When you get 0.2(0.04+0.16+0.16) = 0.072, that’s a joint probability - you haven’t normalized for the conditional case. The <0.31, 0.69> values make sense because they sum to 1.0, showing normalization happened. Check if there’s additional evidence limiting your sample space. You’ll need to divide your calculated values by the total probability of the evidence to get the right conditional distribution. Without seeing the full problem, I’m betting you’re missing a normalization step where you divide by P(evidence) to convert from joint to conditional probabilities.
you’re mixing up joint and conditional distributions. that 0.072 looks right for the joint probability, but p13 needs to be conditioned on whatever evidence the problem gives you. check if there’s a background variable you need to condition on first - that’s where most people get tripped up on these problems.