Grade 7 › G7U10 Probability

Grade 7 › G7U10 Probability › L3
GRADE 7 · ALBERTAOUTCOME AB-G7-SP6

L3 · Theoretical probability: tree diagrams and tables

Learning goal

“I can find the theoretical probability of an event involving two independent events by building a tree diagram or a table, counting the favourable combined outcomes, and dividing by the size of the whole sample space.”

Theoretical probability — the probability worked out by counting equally likely outcomes, before (or without) running any trials: favourable outcomes / total outcomes.
Tree diagram — an organizer that branches: one branch for each outcome of the first event, then one branch for each outcome of the second event off every first branch.
Equally likely — outcomes that have the same chance as each other. Counting works because every combined outcome in the table or tree is equally likely.
Favourable combined outcome — a pair in the sample space that makes the event happen, like (5, 6) when the event is "the dice add to 11."
Worked example

Flip two coins. What is P(both heads)? Step 1: Build the tree. First coin branches: H, T. Off EACH branch, the second coin branches again: H, T. Step 2: The tree has 4 ends - the sample space: HH, HT, TH, TT. All 4 are equally likely. Step 3: Favourable ends for "both heads": only HH - 1 end. Step 4: P(both heads) = 1/4 = 25%. Model both ways: the tree diagram drawn out in words (H -> H, H -> T, T -> H, T -> T), AND the same 4 outcomes as a 2 x 2 table - the tree and the table always agree. Say it plainly: the organizer does the counting honestly. Probability = favourable ends (or cells) / total ends (or cells).

Check yourself — explain it

In the two-coin tree, why are there 4 ends and not 2?

Paired problem — example still visible

Using the same two-coin tree, find P(exactly one head). -> Favourable ends: HT and TH - 2 ends. P = 2/4 = 1/2 = 50%

Faded completion — last step is yours

"Two coins again: P(two tails) = favourable ends / total ends = 1 / ___ = ___." -> 1 / 4 = 1/4

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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