QUIZ 1AND 2.docx - Math 2031 Quiz 1 September 8 201 1 There...

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Unformatted text preview: Math 2031 Quiz 1 September 8, 201'? 1. There are three roads R1,R2,R3 between city A and cityr B. (a) In how many ways can one travel from A to B and back? 0)) List the possibilities in part (a). (c) In how many ways can one travel from A to B and back if a different road is used on the return trip? (d) List the possibilities in in part (c). Ca.) 3.3:.q QL) 3-2::5 (b) 5?: 5?: (a!) I?! lgz P: R: 2: 5'3 RI 3373 R2 E! £2 E; E2 £3 £2 (ix-2 573 RI {821?}: ((73 £2. (9’3 {7: 1‘73 E: £3533 4. A carton of 12 lightbulbs includes 3 that are defective. If2 buibs are chosen at random, what are the probabilities that (a) neither bulb will be defective, (b) exactly 1 bulb will be defective, (:3) both bulbs. '11 be defective? (3 (I: Op) (:3) I?) (’3) c; Q L) (E) (a) 3. A committee consists of 4 men and 6 women. Two 3-person subcommittees A and B are to be formed. (a) How many ways can the two subcommittees be formed? (b) How many of the two subcommittees will be all women? (c) In how many will A be all men and B be all women? (cl) In how #131131 gill A be all women and B be all men? («27 (st-:3 a» (as) (c) (1;) (g) (A) (9(1) 2. (a) How many IO-number sequences can be formed from the numbers 1, 2, 3, 4, 5, 6, 7, 3,9,10? 03» He use a m”. Aer no we flaw-e ow cc. (b) In how many of the sequences in part (a) will the last number be even? (0) How many 4-number subsequences can be formed? (d) If the numbers in part (c) are strung together forming an integer, how many are divisible by 5'? 1’ 62:) (lb; 1 C M‘IEbLééLL‘” 2: 91‘535’3511/0 (1'9) é'ff (a) 20.48“? aflfi‘ Eran: If) ((4') 45.7-4“ 5. A driver’s license exarniner knows that 75% of all applicants have attended a driving school (D). Ifan applicant has attended driving school, the probability of passing (P) the driving test is 0.85, and if an applicant has not attended a driving school (5') , the probability of passing the driving test is 0.60. Given that an applicant passes the driver‘s test, what is the probability that he or she attended a driving school? Rgp) 3—3375“ 22-; Per—CDO 3-25— PPCPIDD : - 915 Fr (F’D’) :*é ,__ P:— PID P:— D Pr (9:17) 2-0» +Fy’véPID") PCD’) g 95") 4 25'} -(r 8'ng 75') +{.é) (“:25") 217.20: I P) = H ’2. - 91' In the following table, 50 college students are classified according to their class standing and also according to their favorite pizza topping. Anchovies (A) Onions (0) Mushrooms (M) Fresh man (F) 6 7 8 Sophomore (S) 2 S 3 Junior (J) 4 8 7 If one of the students is chosen at random, find each of the following. (a) P(0iF) (b) P(F'IA) (C)P(0UM1J') (d) P'IJIAUM) W' _:_r, PCQnF 1213:32— PM: . _, .2? ; L¢3FCD UHIT)’“3{ P£(0Un7nfj_:3§j/§:i % 3 :r’ .3. _LL— PCQ’) (‘9 Pétfl'aum ' 3’9 prim-W”: : 333:2 _________.———————'_' _._— “ qulyHS 32/59 A sample space contains 30 equally Iikely outcomes. Event A contains 12 outcomes, event B contains 10 outcomes, and A n 8 contains 4 outcomes. (a) Draw a corresponding Venn diagram, and find each of the following. (13) HA u B) (c) P(A L.) 3') (cl) P(A’ n B} (e) P(A' m 3') f5" (63) - F?” (b) PffiuB')‘; 36, 1:2 , ,. :21! La) Pram?) "35' (c!) smite-J aha-4’2; Ce) Pm’cg’) 5% Convert each of the following probabilities to odds or odds to probabilities. (a) The probability of rolling a 7' with a pair of fair dice is l 6 . (b) The odds are 3 to 5 that four tosses of a fair coin will result two heads and two tails. _ _i- (a) cit/ZJLZQ flim‘ffifi—h Math 203l Quiz 2 September 22, 2-31? I. A coin is tossed three times. A is the event that two or three heads in a row appear, and Bis the event that either the first or the third toss is a tail, not both. List each of the following. (a) the gamma 513“” (WA (<33 (d) AUB (e) AnB' (2..) Self/(#61, H1??? 4477/) 47717774095 7744-27 7.7791171??? L5) 4: {mac/x, ##7; 77am (6) 5:: {rt/#7": #77; 77/91, 7734;} (J) x4925: imam M7; 77m, #7‘7’,77W} Q3) met: MM} ...
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  • Fall '09
  • Math, Probability theory, #, 5%, 77M

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