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Grade 7 › G7U10 Probability › L2
GRADE 7 · ALBERTAOUTCOME AB-G7-SP5

L2 · Sample space for two independent events

Learning goal

“I can list the complete sample space for an experiment with two independent events - using a table or a systematic list - and I can find its size by multiplying the numbers of outcomes of the two events.”

Sample space — the list of ALL possible outcomes of an experiment. If an outcome is missing from the list, the list is wrong.
Independent events — two events where the result of the first does not change the possible results of the second, like flipping a coin and rolling a die.
Combined outcome — one outcome of the two events together, written as a pair: (Heads, 4) means heads on the coin and 4 on the die.
Systematic list — a list built in an order that guarantees nothing is missed or repeated: fix the first event's result, run through all of the second event's results, then move on.
Worked example

Flip two coins. What are all the possible outcomes? Step 1: Name the two events: Coin 1 and Coin 2. Each has 2 outcomes: H or T. Step 2: Build systematically. Fix Coin 1 = H, run through Coin 2: (H, H), (H, T). Fix Coin 1 = T, run through Coin 2: (T, H), (T, T). Step 3: The sample space is {HH, HT, TH, TT} - 4 combined outcomes. Step 4: Notice that HT and TH are DIFFERENT outcomes: in HT the first coin is heads; in TH the second coin is. Both must be listed. Model both ways: the systematic list, AND a 2 x 2 table with Coin 1 down the side and Coin 2 across the top, one combined outcome in each cell. Say it plainly: a sample space is only useful if it is complete. The systematic order is what makes "complete" checkable.

Check yourself — explain it

Why are HT and TH counted as two different outcomes?

Paired problem — example still visible

Flip a coin and spin a spinner with 3 equal sections (A, B, C). List the sample space. -> (H,A), (H,B), (H,C), (T,A), (T,B), (T,C) - 6 outcomes

Faded completion — last step is yours

"Roll a die and flip a coin. Size of the sample space: 6 x 2 = ___ outcomes." -> 12 outcomes

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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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