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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) 32::5
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£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
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L) (E) (a) 3. A committee consists of 4 men and 6 women. Two 3person 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 IOnumber 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 ﬂawe ow cc.
(b) In how many of the sequences in part (a) will the last number be even?
(0) How many 4number 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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((4') 45.74“ 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 325— PPCPIDD :  915
Fr (F’D’) :*é ,__ P:— PID P:— D
Pr (9:17) 20» +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—
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“ 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,
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La) Pram?) "35' (c!) smiteJ aha4’2;
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.
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(a) cit/ZJLZQ ﬂim‘fﬁﬁ—h Math 203l Quiz 2 September 22, 231? 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'
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 Fall '09
 Math, Probability theory, #, 5%, 77M

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