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Understanding Probability: Basics and Examples

Learn about probability concepts, sample space, and calculating probabilities in various scenarios with clear explanations and examples.

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Understanding Probability: Basics and Examples

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  1. Probability November 2, 2015

  2. SAT Fill-In Question • How many positive factors does the number 120 have? • 120 = 2·2·2·3·5 = 23·31·51 • A factor must have 2s and/or 3s and/or 5s, so let’s draw blanks.

  3. One-Minute Question • How many positive factors does the number 120 have? • 120 = 2·2·2·3·5 = 23·31·51 4 2 2 = 16 For 2s For 3s For 5s

  4. What’s the probability? • How many people are in this class? • If I choose one of you randomly to answer the next question, what’s the probability that I choose you?

  5. What’s the probability? that if I toss 3 coins, exactly one of them will land “heads up”?

  6. What’s the probability? • That if we roll 2 dice, the sum of the dice will be greater than 6?

  7. Probability • A trial is a systematic opportunity for an event to occur. • An experiment is one or more trials.

  8. Probability • The Sample Space is the set of all possible outcomes of an event.

  9. Probability • The probability of an event E, which is a subset of a finite sample space S of equally likely outcomes, is p(E) = .

  10. Probability • In simpler terms, probability is the number of ways you get what you want, divided by the number of ways events could happen.

  11. A candy jar contains 6 peppermint, 4 spearmint, 3 butterscotch and 2 cinnamon candies. • If I select one of these candies at random, what is the probability that I get a spearmint? • N(Sample Space) = 15 candies • N(Success) = 4 • Probability = 4/15

  12. What’s the probability? • That if we roll 2 dice, the sum of the dice will be greater than 6? • So p(>6) = 21/36 = 7/12

  13. If I toss a dart at the target below, what is the probability that I get 20 points? 10 20 30 Radii are 2 inches, 6 inches and 10 inches.

  14. What’s the probability? • How many people are in this class? 22 • If I choose one of you randomly to answer the next question, what’s the probability that I choose you? • 1/22

  15. What’s the probability? that if I toss 3 coins, exactly one of them will land “heads up”? So P(1 H) = 3/8

  16. A candy jar contains 2 spearmint and 2 cinnamon candies. • If I select two of these candies at random, what is the probability that I get both spearmints? • Sample Space = {S1S2, S1C1, S1C2, S2C1, S2C2 C1 C2 } • N(Success) = 1 (The SS) • Probability = 1/6

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