The rules of probability, continuous outcomes and expected counts
Add the probabilities of outcomes that cannot happen together, find which lists can be probabilities, work out a probability as a part of a length, and predict how many times something happens.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- UK: Year 10
- Germany: grade 10
- Iran: grade 11
- Afghanistan: grade 12
- Syria: grade 10
- Palestine: grade 5
- Russia: grade 11
Guide
This studio follows Afghan grade 12 chapter 8 (discrete and continuous sample spaces, probability on a continuous space) and the UK GCSE expected number of outcomes.
The rules: a probability is between 0 and 1, the probabilities of all outcomes add up to 1, and for events that cannot happen together P(A or B) = P(A) + P(B). When an outcome can be any point on a length, the probability of a part is its length divided by the whole length.
Common mistakes worked on here: multiplying where we should add, lists of numbers that do not add up to 1 or contain a negative number, counting a part of a length as a number of outcomes, and mixing up the expected number with the number of trials.