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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.
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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’
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(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