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Probability & Statistics

Probability & Statistics. Course Review. The Idea of Probability. According to the “Book of Odds,” the probability that a randomly selected U.S. adult usually eats breakfast is 0.61. Explain what probability 0.61 means in this setting.

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Probability & Statistics

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  1. Probability & Statistics Course Review

  2. The Idea of Probability According to the “Book of Odds,” the probability that a randomly selected U.S. adult usually eats breakfast is 0.61. • Explain what probability 0.61 means in this setting. • Why doesn’t this probability say that if 100 U.S. adults are chosen at random, exactly 61 of them usually eats breakfast?

  3. Probability Models Create a probability distribution for the event: “You roll two 6-sided die and add the numbers.” P(5) = P(not 5) = P(6) =

  4. Mutually Exclusive or Disjoint

  5. Applying Probability Rules Age of Those Enrolled in Distance-learning Courses Age (yr): 18 to 23 24 to 29 30 to 39 40+ Probability: 0.57 0.17 0.14 0.12 • Why is this a legitimate probability model? • P(not 18 to 23) =

  6. Applying Probability Rules (cont.) A = cholesterol of 240mg or above B = cholesterol of 200mg to 239mg P(A) = 0.16 P(B) = 0.29 • Why are events A and B mutually exclusive? • P(A or B) = • What does P(A or B) mean? • P(cholesterol below 200) =

  7. Two-way Tables Pierced Ears Gender Yes No Male 19 71 Female 84 4 • P(pierced ears) = • P(male with pierced ears) = • P(male or pierced ears) =

  8. Venn Diagrams In an apartment complex, 40% of residents read USA Today. Only 25% read the New York Times. Five percent of residents read both papers. • Make a two-way table • Make a Venn diagram • P(reads at least one newspaper) = • P(does not read newspaper) =

  9. Conditional Probability Pierced Ears Gender Yes No Male 19 71 Female 84 4 • P(male | pierced ears) = • P(pierced ears | male) =

  10. Conditional Probability (cont.) Grade Average School A B Below B Liberal Arts 2142 1890 2268 Physical Sciences 368 432 800 Social Sciences 882 630 588 • P(below B) = • P(physical science | below B) = • P(below B | physical science) =

  11. Independence Dominant Hand Gender Right Left Male 20 3 Female 23 4 Are the events “male” and “left-handed” independent?

  12. More Independence In a deck of cards… Are “1st card is a heart” and “2nd card is a heart” independent? Is this still true if you put the 1st card back in the deck and reshuffle after looking at it?

  13. Tree Diagram (Multiplication Rule) A company makes desktops and laptops in three different states. California produces 40% of the computers, Texas makes 25%, and New York makes the rest. Of the computers made in California, 75% are laptops. Of those made in Texas and New York, 70% and 50%, respectively, are laptops. Make a tree diagram. P(laptop) =

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