Probability • Topic 3 of 5

Compound Events

A compound event combines simple outcomes, often joined by “or”. For mutually exclusive outcomes (ones that cannot happen together, like drawing a red or a blue marble), add their probabilities — equivalently, add the favorable counts and divide by the total. The complement rule helps with “not” questions: P(not A) = 1 − P(A), which is the same as the favorable count of everything other than A over the total. Make sure the outcomes really cannot overlap before adding. The SAT uses these in marble, card and spinner contexts, where adding counts first and dividing once is the cleanest approach.

A bag of 3 red, 4 blue and 5 green marbles with a dashed loop around the red and blue onesCompound eventsP(red or blue) = (3 + 4)/12

✅ Solved examples

1. A bag has 3 red, 4 blue, 5 green. P(red or blue)?
(3 + 4)/12 = 7/12.
2. Using the same bag, P(not green)?
Not green is 7 of 12: 7/12.
3. A die is rolled. P(1 or 2)?
2 of 6 = 1/3.
4. A bag has 5 red, 5 blue. P(red or blue)?
All 10 of 10 = 1.

✏️ Practice — try these, take hints as needed

1. A bag has 2 red, 3 blue, 5 green. P(red or blue)?
Add the two counts.
(2 + 3)/10.
Reduce.
1/2.
2. A die is rolled. P(rolling a 5 or 6)?
2 favorable.
2/6.
Reduce.
1/3.
3. A bag has 4 red, 6 blue. P(not red)?
Not red = blue.
6/10.
Reduce.
3/5.
4. A bag has 3 red, 3 blue, 3 green, 3 yellow. P(red or yellow)?
(3 + 3)/12.
Reduce.
—
1/2.
5. A spinner is 1–8. P(landing on a number greater than 6)?
7 and 8.
2/8.
Reduce.
1/4.

📝 Topic test — 8 questions

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