Hi Mike, Test 7, Section 4, Number 38. Probability: I keep losing track trying to think this through. Other than the table provided, is there a chart I can draw that will help me “see” the probabilities? Or, what’s the best / quickest way to manage this one? Thanks !

Yeah, this chart and the paragraph explaining it are pretty confusing.

A rewording of the question would make it a lot easier to follow. The question should say: “If a contestant who received a score of 5 on any day is selected at random, what is the probability that the contestant did so on Day 2 or Day 3?”

So here’s the proportion you need to fill in:

The question tells you that no contestant received the same score on two different days. That’s important because it means if you got a score of 5 on one day, you didn’t get a score of 5 on any other day. So nobody Ken Jennings’d it—there were 7 scores of 5 in total, and 7 different people got them. So the denominator of the probability is 7—there are only 7 contestants who could be chosen at random who received a score of 5, period.

The numerator is the sum of the number that received a score of 5 on Day 2 (that’s 2 people) and the number that received a score of 5 on Day 3 (that’s 3 people). So the numerator is .

Putting it all together: