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Learn · Numeracy · 4 min

Probability, from scratch

Probability is just how likely something is — a number from 0 to 1:

See it: probability = wanted out of total

0 · impossible½ · even chance1 · certain

P(win) = 38 = 0.38 = 38%

The one move: wanted over total

A bag has 3 red and 5 blue marbles. What’s the chance of drawing red?

  • ① Wanted (red) = 3
  • ② Total marbles = 3 + 5 = 8
  • ③ P(red) = 38 = 0.375 = ≈ 38%

Tips & tricks

The formula
P(event) = wantedtotal — count the outcomes you want over all equally-likely outcomes.
The opposite (complement)
P(NOT it) = 1 − P(it). On a die, P(not a 6) = 1 − 16 = 56.
It never leaves 0–1
0 = impossible, 1 = certain. If you get more than 1, something’s wrong.
Three ways to say it
P = 14 = 0.25 = 25%

Bonus — overlap problems (Venn diagrams)

When two groups overlap (some do both), a Venn diagram untangles them. Say 30 students: 18 play soccer, 12 play basketball, 10 play both.

See it: sort the two groups with a Venn diagram

SoccerBasketball8102none: 10

only soccer 8 · both 10 · only basketball 2 · none 10

The method — fill the middle first

  • ① Both goes in the middle = 10
  • ② Only soccer = 18 − 10 = 8  ·  only basketball = 12 − 10 = 2
  • ③ At least one = 8 + 2 + 10 = 20  (same as 18 + 12 − 10)
  • ④ None = 30 − 20 = 10
  • Then any probability follows — e.g. P(plays soccer) = 1830.

Now you try — 0/4

1. A bag has 3 red and 5 blue marbles. What is P(red)?

2. You roll a normal 6-sided die. What is the chance of rolling a 4?

3. On that die, what is the chance of NOT rolling a 6?

4. In a class of 30: 18 play soccer, 12 play basketball, 10 play both. How many play NEITHER?

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