DO NUMBER P.409#8,12,14 AND SHOW AND EXPLAIN HOW YOU GOT ANSWER

Section 8.6 Independent Events 409 are mutually exclusive, they cannot occur simultaneously. Although these two concepts are not the same, we can draw some conclusions about their relationship. If E and F are mutually exclusive events with positive probabilities, then P(EnF) = 0 / P(E)P(F) since P(E) > 0 andP(F) > 0 which shows that E and F are dependent. In short, mutually exclusive events with pos- itive probabilities must be dependent. Another way of saying this is that independent events with positive probabilities are not mutually exclusive. PROBLEMS 8.6 1. If events E and F are independent with P(E) = ; and independent or dependent. (See page D of the July 21, 1991, P(F) = -, find each of the following. issue of USA TODAY for the article "Pests Now Appearing at a Theater Near You".) (a) P(EnF) (b) P(EUF) (C) P(E | F) (d) P(E [ F) (e) P(EnP) (1) P(EUF) Table 8.12 Theater Patrons (@) P(E| F) Male Female Total 2. If events E, F, and G are independent with P(E) = 0.1, P(F) = 0.3, and P(G) = 0.6, find each Talkers 10 70 of the following Crunchers 25 80 (a) P(EnF) (b) P(Fn G) Seat kickers 15 10 25 (c) P(EnFnG) (d) P(E [ (FnG)) Total 130 45 175 (e) P(E'nFn G) 3. If events E and F are independent with P(E) = } and 9. Dice Two fair dice are rolled, one red and one green, and P(EnF) = $, find P(F). the numbers on the top faces are noted. Let event E be "number on red die is neither I nor 2 nor 3" and event F be "sum is 7"- 4. If events E and F are independent with P(F [ F) = ), find Determine whether E and F are independent or dependent. P(E). 10. Cards A card is randomly drawn from an ordinary deck In Problems 5 and 6, events E and F satisfy the given conditions. of 52 cards. Let E and F be the events "red card drawn" and "face Determine whether E and F are independent or dependent. card drawn" respectively. Determine whether E and F are independent or dependent. 5. P(E) = ]. P(F) = 4, P(En F) = + 11. Coins If two fair coins are tossed, let E be the event "at 6. P(E) = 0.28, P(F) = 0.15, P(En F) = 0.038 most one head" and F be the event "exactly one head". Determine 7. Stockbrokers Six hundred investors were surveyed to whether E and Fare independent or dependent. determine whether a person who uses a full-service stockbroker 12. Coins If three fair coins are tossed, let E be the event "at has better performance in his or her investment portfolio than one most one head" and F be the event "at least one head and one who uses a discount broker. In general, discount brokers usually tail". Determine whether E and Fare independent or offer no investment advice to their clients, whereas full-service dependent. brokers usually offer help in selecting stocks but charge larger 13. Chips In a Bowl A bowl contains seven chips numbered fees. The data, based on the past 12 months, are given in Table 8.1 1. Determine whether the event of having a full-service from 1 to 7. Two chips are randomly withdrawn with replacement. Let E. F. and G be the events broker and the event of having an increase in portfolio value are independent or dependent. F = 3 on first withdrawal Table 8.11 Portfolio Value F = 3 on second withdrawal Increase Decrease Total G = sum is odd Full service 320 400 (a) Determine whether E and Fare independent or dependent. Discount 160 200 (b) Determine whether E and G are independent or dependent. Total 480 (c) Determine whether F and G are independent or dependent. (d) Are E, F, and G independent? 8. Cinema Offenses An observation of 175 patrons in a 14. Chips In a Bowl A bowl contains six chips numbered theater resulted in the data shown in Table 8.12. The table shows from 1 to 6. Two chips are randomly withdrawn. Let E be the three types of cinema offenses committed by male and female event of withdrawing two even-numbered chips and let F be patrons. Crunchers include noisy eaters of popcorn and other the event of withdrawing two odd-numbered chips. morsels, as well as cold-drink slurpers. Determine whether the (a) Are E and F mutually exclusive? event of being a male and the event of being a cruncher are (b) Are E and F independent