WIR Math 141-copyright Joe Kahlig, 08A Page 1Week in Review #7Section 7.5: Conditional Probability and Independent Events.Section 7.6: Bayes’ Theorem.• TO CONVERT CONDITIONAL PROBABILITY TO REGULAR PROBABILITY.• P (B|A) =P (B ∩ A)P (A)• probability of the event B occurring knowing that the event A has already occurred.• A and B are independent events if and only if P (A ∩ B) = P (A)P (B)1. A clothing company selected 1000 persons at random and surveyed them to determine arelationship between age of purchaser and annual purchases of jeans. The results are givenin the table. A person from the survey is s elected at random.(a) What is the probability that the personis under 12 if they purchases 3 or morepairs of jeans annually.(b) What is the probability that the personpurchases 2 pairs of jeans annually if weknow they are older than 25.(c) What is the p robability that the personis younger than 19 given they purchase0 or 1 pair of jeans annually.Jeans Purchased AnnuallyAge 0 1 2 3 or More TotalsUnder 12 60 70 30 10 17012-18 30 100 100 60 29019-25 70 110 120 30 330Over 25 100 50 40 20 210Totals 260 330 290 120 10002. S is the sample space with events: E, F, and G. Use this information to answer these questions.S = {s1, s2, s3, s4, s5, s6, }E = {s1, s2, s5, s6}F = {s2, s4, s5}G = {s3, s5}outcome s1s2s3s4s5s6prob.2297291291129629229(a) P (F |E) =(b) P (G|F ) =WIR Math 141-copyright Joe Kahlig, 08A Page 23. Use the Venn Diagram to answer the following.(a) P (E|F ) =(b) P (FC|E) =0.30.2E F0.4.14. Fill in the missing values of the tree and then answer the following.(a) P (B ∩ E) =(b) P (E|C) =(c) P (E) =(d) P (A ∪ F ) =(e) P (C|E) =(f) Are the events B and E independent?Justify your answer.(g) Are the events A and E independent?Justify your answer.FBEFEAEFC0.50.10.30.60.720.28WIR Math 141-copyright Joe Kahlig, 08A Page 35. Two cards are drawn from a standard deck of cards without replacement. What is theprobability that the first card is a club if the second card is a club?6. Two cards are drawn from a standard deck of cards without replacement. What is theprobability that the first card is an Ace if the second card is a diamond?7. A buildin g on campus has three vending machines: two coke machines and a snack machine.Based on the model of the machines, the first coke m achine has a 12% chance of breakingdown in a p articular week and the second coke machine has a 4% chance of breaking downin a particular week. The snack machine has a 10% chance of breaking down in a particularweek. Assuming independence, find the probability that exactly one machine breaks down.WIR Math 141-copyright Joe Kahlig, 08A Page 48. The following information was compiled regarding married couples living in single-familydwellings. It was found that in 30% of these households, both the husband and the wifeworked, and that 10% of these couples were r enting. In 50% of the h ouseholds, only thehusband worked, and 20% of these couples were renting. In 15% of the households, only thewife worked, and 70% of these couples were renting. In the households where neither worked,95% were renting. A couple from this group is selected at random.(a) Find the probability thatthis couple is renting.(b) What is the probability that onlythe husband works and the coup leowns their house?(c) If the couple is renting, find theprobability that only the wifeis working.9. An auto insurance company classifies its drivers as good risk, medium risk or bad risks. Thetable shows the percent of the drivers in these classifications and the probability that a driverin that classification will have an accident dur ing th e next year. A driver is selected barrandom.(a) What is the probability that the driver will havean accident in the next year?(b) What is the probability that the driver is ratedas a medium risk if they had an accident in thenext year?(c) What is the probability that th e driver is ratedas a bad risk and they did not have an accidentin the next year.Classification drivers(%) Accident(%)go od 50 2medium 35 5bad 15 12WIR Math 141-copyright Joe Kahlig, 08A Page 5Section 8.1: Distribution of Random variables.• A random variable is a rule that assigns a number to each outcome of an experiment.• finite discrete: takes on a finite number of values(skips values).• infinite discrete: takes on an infinite number of values(skips values).• continuous: takes on any value in an interval.• probability distribution• a histogram is a probability distribution represented by a graph(chart).10. Classify the random variable as finite discrete, infinite discrete or continuous and give thevalues of the random variable.(a) You toss a coin and X = the number of tosses until the first head occurs.(b) A football team p lays twelve games in a regular season and X = the number of gamesthe team w ins.(c) X = the temperature of a fish tank in your house.(d) X = the number of minutes that you slept in your math class on a particular class day.11. A box has 2 green, 2 red and 5 yellow balls. A sample of 6 balls are drawn without replacingthe balls drawn. Let the random variable X be the number of yellow balls drawn.(a) Give the range of values that the random variable X may assume.(b) Find the probability distribution of X.(c) Draw the histogram of X.(d) P (X = 4) =(e) P (X < 4) =WIR Math 141-copyright Joe Kahlig, 08A Page 612. You pay $2.00 to play a game. The game consists of flippin g two coins. If both coins areheads, then you get to s pin the spinner on the left for the dollar amount that you win. If bothcoins are tails, then you get to spin the spinner on the right for the dollar amount that youwin. All other results for the coins means that you lose the game. Assum e that the sectionsin each respective s pinner are equal. Let the random variable X be your net winnings whenyou play the game one time. What is the probability distribution for this game.356
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