PROBABILITY STATISTICS Course Review THE IDEA OF PROBABILITY

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. a) Explain what probability 0. 61 means in this setting. b) Why doesn’t this probability say that if 100 U. S. adults are chosen at random, exactly 61 of them usually eats breakfast?

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) =

MUTUALLY EXCLUSIVE OR DISJOINT

APPLYING PROBABILITY RULES Age of Those Enrolled in Distance-learning Courses Age (yr): Probability: a) b) 18 to 23 0. 57 24 to 29 0. 17 30 to 39 0. 14 Why is this a legitimate probability model? P(not 18 to 23) = 40+ 0. 12

APPLYING PROBABILITY RULES (CONT. ) A = cholesterol of 240 mg or above B = cholesterol of 200 mg to 239 mg P(A) = 0. 16 P(B) = 0. 29 a) b) c) d) Why are events A and B mutually exclusive? P(A or B) = What does P(A or B) mean? P(cholesterol below 200) =

TWO-WAY TABLES Gender Male Female a) b) c) Pierced Ears Yes No 19 71 84 4 P(pierced ears) = P(male with pierced ears) = P(male or pierced ears) =

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. a) b) c) d) Make a two-way table Make a Venn diagram P(reads at least one newspaper) = P(does not read newspaper) =

CONDITIONAL PROBABILITY Gender Male Female a) b) Pierced Ears Yes No 19 71 84 4 P(male | pierced ears) = P(pierced ears | male) =

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 a) b) c) P(below B) = P(physical science | below B) = P(below B | physical science) =

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

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

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) =