Math PicnicFree printable practice

Probability worksheets

The chance of one thing happening is how many ways it can, over how many ways anything can. These free printable worksheets describe a bag of colored counters and ask for the probability as a fraction in its simplest form.

Customize Save as PDF New questions

Kid stuck on one? You don’t just get the sheet.

See it worked step by step →
Probability
Probability worksheet — One event, simplified fraction, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Four blue counters in a bag of twelve gives 4/12, which is 1/3. Both steps matter and only the second one is arithmetic: the first is deciding what the denominator is. A child who counts the blue ones and the red ones and writes 4/8 has used the wrong whole, and it is the mistake that survives longest.

Why this sheet works

Some questions ask for the chance of something NOT happening, which is the same count read the other way. Eight of twelve are not blue, so the answer is 2/3 — and noticing that it is one minus the first answer is the beginning of a rule worth having.

How this one works

One question from this sheet, worked through a step at a time.

6 red, 4 blue, 2 green — P(not green)

6 + 4 + 2=12
6 + 4 + 2=12
green:2
not green:12 − 2 =10
6 + 4 + 2=12
not green:10
+=
which is1
6 + 4 + 2=12
=
  1. Count EVERYTHING first, before the ones being asked about: 6 + 4 + 2 = 12 altogether. That is the bottom of the fraction, and it is the half that gets swapped for the wrong number.
  2. Read the question again: it asks for NOT green. So the wins are everything ELSE in the bag — all 12 of them except the 2 green, which is 12 − 2 = 10.
  3. Chance is the wins OVER the total — not over the rest. So it is 10 out of 12.
  4. Check it: the chance of green and the chance of not green have to fill the bag between them. 2 out of 12 and 10 out of 12 make 12 out of 12 — the whole bag, which is 1. If they do not add up, one of the two counts is wrong.
  5. And 10/12 can be written in bigger pieces: 5/6.

Pick another skill