Probability • Topic 1 of 5

Theoretical Probability

Theoretical probability is found by reasoning about equally likely outcomes: it is the number of favorable outcomes divided by the total number of possible outcomes. For a bag of marbles, the probability of drawing a given colour is that colour’s count over the total count, written as a fraction in lowest terms. Every probability lies between 0 and 1. Always count the total carefully — it is the sum of every outcome, not just the unfavourable ones — and reduce the fraction. The SAT often asks for the answer as a reduced fraction, so simplifying is part of getting it right.

A jar holding 3 red and 5 blue marbles, with the probability of red shown as 3 over 8Theoretical probabilityP(red) = 3/8

✅ Solved examples

1. A bag has 3 red and 5 blue marbles. P(red)?
Favorable 3, total 8, so 3/8.
2. A die is rolled. What is P(rolling a 4)?
One favorable out of six: 1/6.
3. A bag has 4 red, 4 blue, 4 green. P(green)?
4 favorable of 12 total = 4/12 = 1/3.
4. A spinner has 8 equal sections, 2 are red. P(red)?
2/8 = 1/4.

✏️ Practice — try these, take hints as needed

1. A bag has 2 red and 3 blue marbles. P(red)?
Favorable over total.
Total = 5.
—
2/5.
2. A die is rolled. P(rolling an even number)?
Even outcomes: 2, 4, 6.
3 of 6.
Reduce.
1/2.
3. A bag has 5 red and 5 green. P(green)?
5 of 10.
Reduce.
—
1/2.
4. A spinner has 10 equal sections, 3 are blue. P(blue)?
3 of 10.
—
—
3/10.
5. A bag has 6 red, 2 blue, 4 yellow. P(blue)?
Total = 12.
2/12.
Reduce.
1/6.

📝 Topic test — 8 questions

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