Conditional probability from a two-way table, and what it tells you
The condition picks a row or a column, and that becomes your denominator. Then compare it against the overall rate to decide whether the two things are related.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
150 patients tested a medication.
Old medication: 24 no improvement, 51 improvement.
New medication: 21 no improvement, 54 improvement.
What is the probability a randomly chosen patient showed improvement? Give the decimal.
Same 150 patients. Old: 24 no improvement, 51 improvement. New: 21 no improvement, 54 improvement.
What is the probability of improvement given the patient took the new medication? Give the decimal.
Overall improvement is 0.70; improvement given the new medication is 0.72.
Is there evidence the new medication makes improvement much more likely? Type yes or no.
Seventy items sold at an open house, by buyer and type.
T-shirt: 18 student, 21 parent. Sweatshirt: 17 student, 14 parent.
One item is chosen at random. Give answers as decimals.
The condition's total
The joint
The conditional
Three answers, three denominators
Same cell of 21, three different questions: 21/70 = 0.3 for the joint, 21/35 = 0.6 for the conditional, and P(parent) = 35/70 = 0.5 for the margin.
The numerator barely moves. Reading which denominator the question wants is the entire skill, and it is worth naming it to yourself before you divide.