# How could this NYT graphic be improved?

Does this image show conditional probabilities of the form Pr[ woman says their relationship is in trouble | woman does the majority of the dishwashing ] = 0.41 and Pr[ woman says their relationship is in trouble | dishwashing is equally shared ] = 0.2?

How could the visualization be improved? It wasn't immediately obvious (to me, at least) that the percentages in the figure are conditional probabilities. [Edit: they aren't! I incorrectly read the rows as being mutually exclusive.]

(Screenshot taken from https://www.nytimes.com/2020/02/13/opinion/sunday/marriage-housework-gender-happiness.html)

• It seems like they’re trying to present it as conditional probability, yet I think it’s a joint probability: the probability that a couple has discussed separating AND the woman does the majority of the dishwashing is $0.24$. – Dave Feb 16 at 1:58
• @Dave that was my initial interpretation, but don't the percentages in the figure sum to more than 100%? If so, the numbers can't be a joint probability distribution. – Adrian Feb 16 at 2:01
• They could sum to over 100%. Consider what happens if you have a row about discussing having children where perhaps over 50% of each column could have had such a discussion. – Dave Feb 16 at 2:12
• Ah, true, the rows are not mutually exclusive (at least, they aren't mutually exclusive by definition, but they could be depending on how the survey was structured). – Adrian Feb 16 at 2:48