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Probability Basics

Probability Basics. Chapter 14 Basic concepts and vocabulary. Things we will cover. Probability Sample Space Probability Assignment Rule Complement Rule Addition Rule Multiplication Rule. Probability Basics. The probability of an event is a number between 0 and 1

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Probability Basics

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  1. Probability Basics Chapter 14 Basic concepts and vocabulary

  2. Things we will cover. Probability Sample Space Probability Assignment Rule Complement Rule Addition Rule Multiplication Rule

  3. Probability Basics The probability of an event is a number between 0 and 1 It reports the likelihood of an event’s occurrence.

  4. Probability Assignment Rule“the duh rule” 0 ≤ P ≤ 1 and ∑P = 1

  5. Complement Rule Suppose that P(on time) = P(T) = 0.85 What’s P(not on time) ? P(not on time) = P(TC) = 1 – P(T) = 0.15 Because P(T) + P(TC) = 1

  6. Addition Rule The 2 events cannot happen at the same time. One excludes the other from happening! Suppose that S stands for a Sophomore and J stands for Junior. The probability of a randomly selected student is a Sophomore is 0.4 and the probability of a student being a Junior is 0.32. The P(S or J) = Must be Disjoint

  7. Multiplication Rule The 2 events cannot affect the probability of each other. One does not effect the other happening. Suppose that F stands for a green light on the first day and S stands for a green light the 2nd day. The probability of getting a green light is 0.75. The probability of hitting green lights on 2 consecutive days is… The P(F and S) = Must be Independent

  8. Class practice • Make sure you are logged into the calculator and open 80- class practice.

  9. In class practice: • You roll a fair die three times. What is the probability that . . . 1) you roll all 5’s?

  10. In class practice: • You roll a fair die three times. What is the probability that . . . 2) you roll all odd numbers?

  11. In class practice: • You roll a fair die three times. What is the probability that . . . 3) none of your rolls gets a number divisible by 3?

  12. In class practice: • You roll a fair die three times. What is the probability that . . . 4) you roll at least one 5?

  13. In class practice: • You roll a fair die three times. What is the probability that . . . 5) The numbers you roll are not all 5’s?

  14. Census reports for a city indicate that 62% of the residents classify themselves as Christian, 12% as Jewish, and 16% as member's of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach . . . 6) all Christians?

  15. Census reports for a city indicate that 62% of the residents classify themselves as Christian, 12% as Jewish, and 16% as member's of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach . . . 7) no Jews?

  16. Census reports for a city indicate that 62% of the residents classify themselves as Christian, 12% as Jewish, and 16% as member's of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach . . . 8) at least one person who is nonreligious?

  17. A few years ago M&M’s decided to add a new color and conduct a global survey. In Japan they found that 38% chose pink, 36% teal and 16% chose purple and 10% had no preference Check to see if probabilities are legitimate – check to see if all are between 0 and 1 check the “duh” rule – all add to 1 (probability assignment rule) They don’t pass the “duh” rule so create a final category.

  18. What’s the probability a random respondent preferred either pink or teal? The word “either” suggest the addition rule or P(A + B). Check if disjoint. P(pink or teal) = P(pink) + P(teal) = 0.38 + 0.36 = 0.74

  19. What’s the probability that 2 random respondents both picked purple? The word “both” suggest the multiplication rule or P(A and B). Check for independence. P(both purple) = P(1st picks purple) x P(2nd picks purple) = 0.16 x 0.16 = 0.0256

  20. What’s the probability that out of 3 random respondents at least 1 picked purple? The words “at least 1” suggest the complement rule or P(A) = 1 – P(Ac) Check for independence. P(not purple) = 1 – P(purple) = 1 – 0.16 = 0.84 P(none picking purple) = (0.84)3 = 0.5927 P(at least 1 purple) = 1 – P(none picked purple) = 1 – 0.5927 = 0.4073

  21. And Finally:The probability of an event is its long term relative frequency found by . . . 1- Looking at many replications(repeats) of an event 2- Deducing it from equally likely events 3- Using some other information (the catch all)

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