Simple Probability

Learn equally likely probability, complement events.

Lesson 3 of 32 parts Practice Flashcards

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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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Equally Likely Probability

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

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.

Complement Events

Objective: Explain complement events, apply the stated method, and check its conditions.

The complement Aᶜ contains all outcomes not in A. Since an event and its complement partition the sample space, P(Aᶜ)=1−P(A). The complement depends on the complete stated outcome space, including every possible alternative. Include every alternative in the stated sample space.

Formulas

$P(Aᶜ)=1−P(A)$

Worked examples

Try itA bag has 42 red and 49 blue counters. Find P(not red) for one uniform draw.Show answer

Step 1: Not red means blue in this two-color bag. Step 2: Use 49/(42+49). Step 3: The probability is 7/13.

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