Probability and data

This topic gathers the statistics ideas that SAT, ACT, GCSE and IB papers test again and again. It starts with combining probabilities. When a question needs two things to both happen, you multiply along the path, and when either finished outcome will do, you add. A probability above 1 is the quick sign that something was added that should have been multiplied. The second page is about independence. Multiplying P(A) by P(B) only works when one event doesn't change the chance of the other, so drawing without replacement needs the updated second chance. You can test independence from data by checking whether P(A and B) equals P(A) × P(B). The last page covers cumulative frequency graphs. Each running total is plotted at the upper boundary of its class, and the median and quartiles are read across at half and a quarter of the total. Work through the pages in order and say out loud whether each step is an and or an or before you calculate.