Sample Spaces

Learn sample spaces and counting, equally likely probability.

Lesson 1 of 32 parts Practice Flashcards

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Sample Spaces and Counting

Objective: Explain sample spaces and counting, apply the stated method, and check its conditions.

A sample space lists elementary outcomes of a chance process. For staged independent equally likely choices, outcome counts multiply. If stage choices have unequal probabilities, total count alone does not establish equal outcome chances; define the elementary outcomes explicitly. Outcome counting requires checking likelihood assumptions before computing probability.

Formulas

For m then n choices: mn ordered outcomes

Worked examples

Try itA spinner has 6 equally likely sectors and an independent numbered spinner has 7 equally likely sectors. How many ordered outcomes?Show answer

Step 1: Choose one sector from each spinner. Step 2: Use the multiplication principle 6·7. Step 3: There are 42 equally likely ordered outcomes.

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Sample Spaces and Counting

Objective: Explain sample spaces and counting, apply the stated method, and check its conditions.

Formulas

For m then n choices: mn ordered outcomes

Worked examples

Try itA spinner has 6 equally likely sectors and an independent numbered spinner has 7 equally likely sectors. How many ordered outcomes?Show answer

Step 1: Choose one sector from each spinner. Step 2: Use the multiplication principle 6·7. Step 3: There are 42 equally likely ordered outcomes.

Equally Likely Probability

Objective: Explain equally likely probability, apply the stated method, and check its conditions.

For a finite equally likely sample space, probability is favorable outcome count divided by total count. Probabilities lie from zero to one inclusive. The counting shortcut requires equally likely elementary outcomes, not merely a list of event labels. Favorable-over-total requires equally likely outcomes.

Formulas

P(A)=favorable/total for equally likely outcomes

Worked examples

Try itA bag has 42 red and 49 blue counters. One counter is drawn uniformly. Find P(red).Show answer

Step 1: Count favorable counters and total counters. Step 2: Use 42/(42+49). Step 3: P(red)=6/13.

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