SAMPLE. Chapter 9 PROBABILITY EXERCISE 9A.1 EXERCISE 9A.2. ¼ 0:78 b P(on a line) = 1 a P(inside a square) = 113

Transcription

1 Chpter 9 ROAILIY EXERCISE 9A. (insie squre) = ¼ 0:78 (on line) = ¼ 0: otl frequeny =7+8+9+=78 (0 to 9 seons) = 8 78 ¼ 0:87 (> 0 seons) = 78 ¼ 0:0 (etween 0 n 9 seons inlusive) = Clls/y No. of ys otl frequeny = = 90 EXERCISE 9A ¼ 0:7 Survey lste =ys i (0 lls) ¼ ¼ 0:0 ( ys gp) ¼ 7 90 ¼ 0:089 (femle t C is smoker) = 9 ¼ 0: At shool E, there re = 79 yer ol stuents. 7+=of these smoke, so 79 = 8 o not smoke. ) (stuent t E is not smoker) = 8 79 ¼ 0:8 8 + (he or she is smoker) = 0 + ¼ 0: (> lls) ¼ ++0+ ¼ 0:8 (omplint in 008=09 out ustomer servie) = ¼ 0: (omplint out illing) = ¼ 0: (not relte to either illing or fults in 009=0) = ¼ 0: 909 i (Fe y in Auurn is > ± C)= : 8 ¼ 0:89 (Fe y in Auurn is < 0 ± 8 : C)= =0: 8 (emperture > 0 ± C on summer y) = 9:+:+: (It is Jn given it is 0 ± : C y) = 0:+:+0:7 ¼ 0: i (< lls) ¼ +7+ ¼ 0: (t lest ys gp) ¼ ¼ 0: ¼ 0:8

2 Mthemtil Stuies SL (r en), Chpter 9 ROAILIY 9 EXERCISE 9 fa,, C, Dg Let enote oy n G enote girl. f, G, G, GGg facd, ADC, ACD, ACD, ADC, ADC, ACD, ADC, CAD, CDA, DAC, DCA, CAD, CAD, CAD, CDA, CDA, CDA, DAC, DAC, DAC, DCA, DCA, DCAg Let enote oy n G enote girl. f, G, G, G, GG, GG, GG, GGGg oin ie D C ie A ie A C D ie Let enote hes n -ent 0-ent Let enote hes n oin A enote enote tils. tils. C X Let enote pink, Y enote lue, n Z enote X white. Y Z X Y Z EXERCISE 9C. otl numer of mrles =++7= (re) = = (green) = = (lue) = 7 (not re) = +7 = = e (neither green nor lue) =(re) = = f (green or re) = + = 8 8 re rown n so re white. i (rown) = 8 = (white) = = st tiket A C n tiket (multiple of ) = (, 8,,, 0,, 8,, ) = 9 (etween n 9 inlusive) = (, 7, 8, or9) = = = 9

3 9 Mthemtil Stuies SL (r en), Chpter 9 ROAILIY (> 0) = (,,,,...,, ) 0 = = = 9 f (o multiple of ) = (, 9,,, 7, or) = = (9) = e (multiple of ) = ( or ) = = 8 g (multiple of n ) = (multiple of ) = (,, ) = h (multiple of or ) = (,, 8,,, 8, 0,, 8, 0,, ) = = = (on uesy) = 7 (on weeken) = 7 = (in July) + = fover yer periog (in Jnury or Ferury) = + fover yer perio, rememer lep yersg = 7 = Let A enote Antti, K enote Ki, n N enote Ne. ossile orers re: fakn, ANK, KAN, KNA, NAK, NKAg i (A in mile) = = (A t left en) = = i (A not t right en) = = iv (K n N re together) = = Let G enote girl n enote oy. ossile orers re: f, G, G, GG, G, GG, GG, GGGg i (ll oys) =() = 8 (ll girls) =(GGG) = 8 i (oy, then girl, then girl) = (GG) = 8 iv ( girls n oy) = (GG or GG or GG) = 8 v (girl is elest) vi (t lest one oy) = (G or GG or GG or GGG) = 8 = = 7 8 fll exept GGGg 7 facd, ADC, ACD, ACD, ADC, ADC, ACD, ADC, CAD, CDA, DAC, DCA, CAD, CAD, CAD, CDA, CDA, CDA, DAC, DAC, DAC, DCA, DCA, DCAg i (A sits on one en) = = ( sits on one of the two mile sets) = = i (A n re together) = = iv (A,, n C re together) = =

4 Mthemtil Stuies SL (r en), Chpter 9 ROAILIY 97 EXERCISE 9C. Let enote hes n enote tils. -ent -ent 0-ent 0-ent ( hes) = ( tils) = -ent -ent 0-ent (extly he) = ( or ) Let enote hes n enote tils. i i ( n ) = 0 oin oin = = oin iv 0-ent (t lest he) =( or or ) oin = here re = 0 possile omine outomes. ( n even) =( or ) = 0 = oin (n o) = 0 = ( or) = 0 = ie ie ie ie ie ie (two s) = ( n ) = = 8 ( or ) = 0 = 9

5 98 Mthemtil Stuies SL (r en), Chpter 9 ROAILIY ie e ie f ie ie ie ie (t lest one ) = (extly one ) = 0 = 8 (no sixes) = EXERCISE 9C., i, i, i ie ie ie ie ie ie (sum is ) = (sum is 8 or 9) = 9 = (result is 0) = (result is ) = 8 = = = ie ie i i i ie ie (sum < ) = 0 = (result is > ) = = ie ie (result is ) = (result is < ) = 7 (result is o) = = EXERCISE 9D. (Ro rolls n Kerry rolls ) = () () fevents re inepenentg = = (Ro rolls o n Kerry rolls > ) = (o) (> ) = (,, or) ( or ) (oth roll > ) = (> ) (> ) = = = =

6 00 Mthemtil Stuies SL (rmthemtil en), ChpterStuies 9 ROAILIY SL (r en), Chpter 9 ROAILIY 99 (, then, then ) = () () () = (, then, then ) = () () () = = 8 = 8 Let A e the event of photoopier A mlfuntioning n e the event of photoopier mlfuntioning. (oth mlfuntion) = (A n ) = (A) () = = = (they will e hppy) = (, then G, then, then G) = () (G) () (G) = = Let J e the event of Jiri hitting the trget n e the event of enit hitting the trget. ) (J) =0:7, (J 0 )=0:, () =0:8, ( 0 )=0: (oth hit) = (J) () =0:7 0:8 =0: (oth work) = (A 0 n 0 ) = (A 0 ) ( 0 ) = = = 0 (they will e unhppy) = (they will e hppy) = = (J hits n misses) = (J) ( 0 ) =0:7 0: =0: (oth miss) = (J 0 ) ( 0 ) =0: 0: =0:0 ( hits n J misses) = () (J 0 ) =0:8 0: =0: Let e the event the rher hits the ullseye. ) () =, (0 )= ( hits) ( hits then miss) (ll misses) = () () () = = 8 = () () ( 0 ) = = = ( 0 ) ( 0 ) ( 0 ) = = 7 EXERCISE 9D. (ll strwerry rems) = (st is S n n is S n r is S) = = (oth re) = (st is R n n is R) = (none re strwerry rems) = (st is S 0 n n is S 0 n r is S 0 ) = 0 = (GR) = (st is G n n is R) = = 7 = 7 0