Multiply ALONG branches, add BETWEEN paths
Probability of a sequence = multiply along its branches. For an event that can happen several ways, add the probabilities of each complete path.
Without replacement changes the second branch
If the item is not replaced, the total and the relevant count both drop by on the second pick, so the second-set probabilities differ from the first.
"At least one" — use the complement
is usually the quickest route.
Drawn from real examiner reports.
Putting integers (not fractions/decimals) on branches
Writing whole-number counts on the branches instead of probabilities, or not to the required accuracy.
Not changing the denominator for "without replacement"
Using the same denominators on the second pick (treating it as with replacement) when items are not replaced.
Counting only one order for "one of each"
For "one red and one blue" you must add both paths (red-then-blue AND blue-then-red).
Adding probabilities to more than 1
Adding probabilities along a single path (instead of multiplying), giving a value greater than 1.
Label the second set of branches
Always label the second-pick branches (and their probabilities) — unlabelled branches lose marks even with correct arithmetic.
Probabilities on each pair of branches add to . Write them as fractions or decimals, never as whole-number counts.
In a decimal-probability context (e.g. on time / late), how do you get the "fail/late" branch if you are told the "on time" probability is ?
A bag has red and blue counters. A counter is taken, its colour noted, and replaced; then a second is taken. Find the probability that both are red.
