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3.13: Sura ya Suluhisho (Mazoezi + Kazi ya nyumbani)

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    179661

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    1.

    1. \(P(L′) = P(S)\)
    2. \(P(M \cup S)\)
    3. \(P(F \cap L)\)
    4. \(P(M|L)\)
    5. \(P(L|M)\)
    6. \(P(S|F)\)
    7. \(P(F|L)\)
    8. \(P(F \cup L)\)
    9. \(P(M \cap S)\)
    10. \(P(F)\)

    3.

    \(P(N)=\frac{15}{42}=\frac{5}{14}=0.36\)

    5.

    \(P(C)=\frac{5}{42}=0.12\)

    7.

    \(P(G)=\frac{20}{150}=\frac{2}{15}=0.13\)

    9.

    \(P(R)=\frac{22}{150}=\frac{11}{75}=0.15\)

    11.

    \(P(O)=\frac{150-22-38-20-28-26}{150}=\frac{16}{150}=\frac{8}{75}=0.11\)

    13.

    \(P(E)=\frac{47}{194}=0.24\)

    15.

    \(P(N)=\frac{23}{194}=0.12\)

    17.

    \(P(S)=\frac{12}{194}=\frac{6}{97}=0.06\)

    19.

    \(\frac{13}{52}=\frac{1}{4}=0.25\)

    21.

    \(\frac{3}{6}=\frac{1}{2}=0.5\)

    23.

    \(P(R)=\frac{4}{8}=0.5\)

    25.

    \(P(O \cup H)\)

    27.

    \(P(H|I)\)

    29.

    \(P(N|O)\)

    31.

    \(P(I \cup N)\)

    33.

    \(P(I)\)

    35.

    Uwezekano kwamba tukio litatokea kutokana na kwamba tukio jingine tayari limetokea.

    37.

    1

    39.

    uwezekano wa kutua juu ya idadi hata au nyingi ya tatu

    41.

    \(P(J) = 0.3\)

    43.

    \(P(Q\cap R)=P(Q)P(R)\)

    \(0.1 = (0.4)P(R)\)

    \(P(R) = 0.25\)

    45.

    0.376

    47.

    C|L inamaanisha, kutokana na mtu aliyechaguliwa ni Mlatino wa California, mtu ni mpiga kura aliyesajiliwa ambaye anapendelea maisha gerezani bila msamaha kwa mtu aliyehukumiwa mauaji ya shahada ya kwanza.

    49.

    L\ cap C ni tukio ambalo mtu aliyechaguliwa ni Latino California amesajiliwa wapiga kura ambaye anapendelea maisha bila parole juu ya adhabu ya kifo kwa mtu na hatia ya mauaji ya shahada ya kwanza.

    51.

    0.6492

    53.

    Hapana, kwa sababu P (L\ cap C) haina sawa 0.

    55.

    \(P(\text { musician is a male } \cap \text { had private instruction) }=\frac{15}{130}=\frac{3}{26}=0.12.\)

    57.

    Matukio sio ya kipekee. Inawezekana kuwa mwanamuziki wa kike aliyejifunza muziki shuleni.

    58.

    Hii ni mchoro wa mti na matawi mawili. Tawi la kwanza, lililoitwa Saratani, linaonyesha mistari miwili: 0.4567 C na 0.5433 C'. Tawi la pili linaitwa Uongo Positive. Kutoka C, kuna mistari miwili: 0 P na 1 P'. Kutoka C', kuna mistari miwili: 0.51 P na 0.49 P'.

    Kielelezo\(\PageIndex{21}\)

    60.

    \(\frac{35,065}{100,450}\)

    62.

    Kuchukua mtu mmoja kutoka kwenye utafiti ambaye ni Kijapani, Marekani na anavuta sigara 21 hadi 30 kwa siku ina maana kwamba mtu anapaswa kukidhi vigezo vyote viwili: wote wa Kijapani, Marekani na huvuta sigara 21 hadi 30. Nafasi ya sampuli inapaswa kujumuisha kila mtu katika utafiti. Uwezekano ni\(\frac{4,715}{100,450}\).

    64.

    Kuchukua mtu mmoja kutoka kwenye utafiti ambaye ni Kijapani wa Marekani kutokana na mtu huyo anavuta sigara 21-30 kwa siku, inamaanisha kwamba mtu lazima atimize vigezo vyote na nafasi ya sampuli imepunguzwa kwa wale wanaovuta sigara 21-30 kwa siku. Uwezekano ni\(\frac{4715}{15,273}\).

    66.

    1. Huu ni mchoro wa mti na matawi yanayoonyesha uwezekano wa kila kuteka. Tawi la kwanza linaonyesha mistari miwili: 5/8 Kijani na 3/8 Njano. Tawi la pili lina seti ya mistari miwili (5/8 Kijani na 3/8 Njano) kwa kila mstari wa tawi la kwanza.

      Kielelezo\(\PageIndex{22}\)

    2. \(P(G G)=\left(\frac{5}{8}\right)\left(\frac{5}{8}\right)=\frac{25}{64}\)
    3. \(P(\text { at least one green })=P(G G)+P(G Y)+P(Y G)=\frac{25}{64}+\frac{15}{64}+\frac{15}{64}=\frac{55}{64}\)
    4. \(P(G | G)=\frac{5}{8}\)
    5. Ndiyo, wao ni huru kwa sababu kadi ya kwanza imewekwa nyuma katika mfuko kabla ya kadi ya pili inayotolewa; muundo wa kadi katika mfuko unabaki sawa kutoka kuteka moja kuteka mbili.

    68.

    1. \ (\ UkurasaIndex {22}\) “>
      <20> 20—64 >64 Jumla
      Mwanamke “class="lt-stats-5549">0.0244 0.3954 64" class="lt-stats-5549">64">0.0661 0.486
      Kiume “class="lt-stats-5549">0.0259 0.4186 64" class="lt-stats-5549">64">0.0695 0.514
      Jumla “class="lt-stats-5549">0.0503 0.8140 64" class="lt-stats-5549">64">0.1356 1

      Jedwali 3.22

    2. \(P(F) = 0.486\)
    3. \(P(>64 | F) = 0.1361\)
    4. \(P(>64 \text{ and } F) = P(F) P(>64|F) = (0.486)(0.1361) = 0.0661\)
    5. \(P(>64 | F)\)ni asilimia ya madereva wa kike ambao ni 65 au zaidi na P (>64\ cap F) ni asilimia ya madereva ambao ni wanawake na 65 au zaidi.
    6. \(P(>64) = P(>64 \cap F) + P(>64 \cap M) = 0.1356\)
    7. Hapana, kuwa wa kike na 65 au zaidi sio pekee kwa sababu wanaweza kutokea kwa wakati mmoja\(P(>64 \cap F) = 0.0661\).

    70.

    1. \ (\ UkurasaIndex {23}\) “>
      Gari, lori au van Tembea Usafiri wa umma Nyingine Jumla
      Alone 0.7318
      Sio peke yake 0.1332
      Jumla 0.8650 0.0390 0.0530 0.0430 1

      Jedwali 3.23

    2. Kama sisi kudhani kwamba walkers wote ni peke yake na kwamba hakuna kutoka makundi mengine mawili kusafiri peke yake (ambayo ni dhana kubwa) tuna:\(P(\text{Alone}) = 0.7318 + 0.0390 = 0.7708\).
    3. Fanya mawazo sawa na katika (b) tuna:\((0.7708)(1,000) = 771\)
    4. \((0.1332)(1,000) = 133\)

    73.

    1. Huwezi kuhesabu uwezekano wa pamoja kujua uwezekano wa matukio yote yanayotokea, ambayo si katika taarifa iliyotolewa; probabilities inapaswa kuzidishwa, si aliongeza; na uwezekano ni kamwe mkubwa kuliko 100%
    2. Nyumbani inayoendeshwa na ufafanuzi ni hit mafanikio, kwa hiyo anapaswa kuwa na angalau hits nyingi za mafanikio kama anaendesha nyumbani.

    75.

    0

    77.

    0.3571

    79.

    0.2142

    81.

    Daktari (83.7)

    83.

    \(83.7 − 79.6 = 4.1\)

    85.

    \(P(\text{Occupation} < 81.3) = 0.5\)

    87.

    1. Utafiti Forum utafiti 1,046 Torontonia.
    2. 58%
    3. 42% ya 1,046 = 439 (kuzunguka kwa integer iliyo karibu)
    4. 0.57
    5. 0.60.

    89.

    1. \(P(\text { Betting on two line that touch each other on the table) }=\frac{6}{38}.\)
    2. \(P(\text { Betting on three numbers in a line })=\frac{3}{38}\)
    3. \(P(\text { Betting on one number })=\frac{1}{38}\)
    4. \(P(\text { Betting on four number that touch each other to form a square) }=\frac{4}{38}.\)
    5. \(P(\text { Betting on two number that touch each other on the table })=\frac{2}{38}\)
    6. \(P(\text { Betting on } 0-00-1-2-3)=\frac{5}{38}\)
    7. \(P(\text { Betting on } 0-1-2 ; \text { or } 0-00-2 ; \text { or } 00-2-3)=\frac{3}{38}\)

    91.

    1. \(\{G1, G2, G3, G4, G5, Y1, Y2, Y3\}\)
    2. \(\frac{5}{8}\)
    3. \(\frac{2}{3}\)
    4. \(\frac{2}{8}\)
    5. \(\frac{6}{8}\)
    6. Hapana, kwa sababu\(P(G \cap E)\) si sawa 0.

    93.

    KUMBUKA

    sarafu toss ni huru ya kadi ilichukua kwanza.

    1. \(\{(G,H) (G,T) (B,H) (B,T) (R,H) (R,T)\}\)
    2. \(P(A)=P(\text { blue }) P(\text { head })=\left(\frac{3}{10}\right)\left(\frac{1}{2}\right)=\frac{3}{20}\)
    3. Ndio, A na B ni za kipekee kwa sababu haziwezi kutokea kwa wakati mmoja; huwezi kuchukua kadi ambayo ni ya rangi ya bluu na pia (nyekundu au kijani). \(P(A \cap B) = 0\)
    4. Hapana, A na C sio pekee kwa sababu zinaweza kutokea kwa wakati mmoja. Kwa kweli, C inajumuisha matokeo yote ya A; ikiwa kadi iliyochaguliwa ni bluu pia ni (nyekundu au bluu). \(P(A \cap C) = P(A) = \frac{3}{20}\)

    95.

    1. \(S = \{(HHH), (HHT), (HTH), (HTT), (THH), (THT), (TTH), (TTT)\}\)
    2. \(\frac{4}{8}\)
    3. Ndiyo, kwa sababu ikiwa A imetokea, haiwezekani kupata mikia miwili. Kwa maneno mengine,\(P(A \cap B) = 0\).

    97.

    1. Ikiwa Y na Z ni huru, basi\(P(Y \cap Z) = P(Y)P(Z)\), hivyo\(P(Y \cup Z) = P(Y) + P(Z) - P(Y)P(Z)\).
    2. 0.5

    99.

    iii i iv ii

    101.

    1. \(P(R) = 0.44\)
    2. \(P(R|E) = 0.56\)
    3. \(P(R|O) = 0.31\)
    4. Hapana, kama fedha zinarudi sio huru ya darasa ambalo fedha ziliwekwa. Kuna njia kadhaa za kuhalalisha hii hesabu, lakini moja ni kwamba fedha zilizowekwa katika madarasa ya uchumi hazirudi kwa kiwango sawa cha jumla;\(P(R|E) \neq P(R)\).
    5. Hapana, utafiti huu haukuunga mkono wazo hilo; kwa kweli, inaonyesha kinyume. Fedha zilizowekwa katika madarasa ya uchumi zilirudishwa kwa kiwango cha juu kuliko mahali pa fedha katika madarasa yote kwa pamoja;\(P(R|E) > P(R)\).

    103.

    1. \(P(\text { type } \mathrm{O} \cup \mathrm{Rh}-)=P(\text { type } \mathrm{O})+P(\mathrm{Rh}-)-P(\text { type } \mathrm{O} \cap \mathrm{Rh}-)\)

      \(0.52=0.43+0.15-P(\text { type } O \cap \mathrm{Rh}-)\); kutatua kupata\(P(\text { type } \mathrm{O} \cap \mathrm{Rh}-)= 0.06\)

      6% ya watu wana aina O, Rh- damu

    2. \(P(\text { NOT (type O } \cap \mathrm{Rh}-) )=1-P(\text { type } \mathrm{O} \cap \mathrm{Rh}-)=1-0.06=0.94\)

      94% ya watu hawana aina O, Rh- damu

    105.

    1. Hebu C = kuwa tukio ambalo cookie ina chokoleti. Hebu N = tukio ambalo cookie ina karanga.
    2. \(P(C \cup N) = P(C) + P(N) - P(C \cap N) = 0.36 + 0.12 - 0.08 = 0.40\)
    3. \(P(\text { NElTHER chocolate NOR nuts) }=1-P(C \cup N)=1-0.40=0.60\)

    107.

    0

    109.

    \(\frac{10}{67}\)

    111.

    \(\frac{10}{34}\)

    113.

    d

    115.

    1. \ (\ UkurasaIndex {24}\) “>
      Mbio na ngono 1—14 15—24 25—64 Zaidi ya 64 JUMLA
      Nyeupe, kiume 210 3,360 13,610 4,870 22,050
      Nyeupe, kike 80 580 3,380 890 4,930
      Nyeusi, kiume 10 460 1,060 140 1,670
      Nyeusi, kike 0 40 270 20 330
      Wengine wote 100
      JUMLA 310 4,650 18,780 6,020 29,760

      Jedwali 3.24

    2. \ (\ UkurasaIndex {25}\) “>
      Mbio na ngono 1—14 15—24 25—64 Zaidi ya 64 JUMLA
      Nyeupe, kiume 210 3,360 13,610 4,870 22,050
      Nyeupe, kike 80 580 3,380 890 4,930
      Nyeusi, kiume 10 460 1,060 140 1,670
      Nyeusi, kike 0 40 270 20 330
      Wengine wote 10 210 460 100 780
      JUMLA 310 4,650 18,780 6,020 29,760

      Jedwali 3.25

    3. \(\frac{22,050}{29,760}\)
    4. \(\frac{330}{29,760}\)
    5. \(\frac{2,000}{29,760}\)
    6. \(\frac{23,720}{29,760}\)
    7. \(\frac{5,010}{6,020}\)

    117.

    b

    119.

    1. \(\frac{26}{106}\)
    2. \(\frac{33}{106}\)
    3. \(\frac{21}{106}\)
    4. \(\left(\frac{26}{106}\right)+\left(\frac{33}{106}\right)-\left(\frac{21}{106}\right)=\left(\frac{38}{106}\right)\)
    5. \(\frac{21}{33}\)

    121.

    a