And / or probability, step by step

"And" and "or" are one word apart and several counters apart.

The question

P(red or round) from red 4 round, 2 square · blue 3 round, 3 square

4 + 2 + 3 + 3=12
4 + 2 + 3 + 3=12
4 + 2 + 3=9
9/12=3/4
  1. Count EVERYTHING first: 4 + 2 + 3 + 3 = 12 counters altogether. That is the bottom of the fraction whichever way the question is asked.
  2. "Or" means a counter counts if EITHER is true, so it is more than one group: 4 + 2 + 3 = 9. Nothing is counted twice — the groups being added do not overlap.
  3. 9 out of 12 is 3/4 in bigger pieces.

How it works.

  1. 01

    Count EVERYTHING first: 4 + 2 + 3 + 3 = 12 counters altogether. That is the bottom of the fraction whichever way the question is asked.

  2. 02

    "Or" means a counter counts if EITHER is true, so it is more than one group: 4 + 2 + 3 = 9. Nothing is counted twice — the groups being added do not overlap.

  3. 03

    9 out of 12 is 3/4 in bigger pieces.