Higher only · conditional probability

Conditional
probability.
“Given that…”

the denominator
shrinks

two words that change the question —

Given that

you already know something happened

so only those outcomes are possible

step 1 of 4

From a Venn diagram

1. Given French: only that circle counts.

2. That is 7 + 5 = 12 students, not 30.

✓ P(German given French) = 512

step 2 of 4

From a two-way table

1. Given they walk: only those 67 count.

2. 45 of those are in Year 10.

✓ The “given” group is the denominator

Y10: 45 walk, 15 do not

Y11: 22 walk, 18 do not

walkers: 45 + 22 = 67

P(Y10 given walks) = 4567

step 3 of 4

On a tree

1. Second branches are conditional.

2. This one: red, given the first was red.

✓ P(red given red) = 24

step 4 of 4

Working backwards

1. Find every route that ends in red.

2. Those routes are the new total.

✓ Wanted route ÷ all routes that fit

second is red. P(first was red)?

R, R = 620B, R = 620

P(second red) = 1220

620 ÷ 1220 = 12

conditional probability —

“Given that”

shrinks the total

Venn or table

use only that row or circle

Tree

second branches are conditional

P(A given B) =
P(A and B) ÷ P(B).

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