Example 14 - Chapter 16 Class 11 Probability

Transcript

Example 14 On her vacations Veena visits four cities (A, B, C and D) in a random order. What is the probability that she visits A before B? 4 cities can be visited in any of following order S = ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CBAD, CDAB, CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA n(S) = 24 Let E be the event that she visits A before B Hence , E = ABCD, ABDC, ADBC, ACDB, ADBC, ADCB, CABD, CADB, CDAB, DABC, DACB, DCAB, Hence , E = ABCD, ABDC, ADBC, ACDB, ADBC, ADCB, CABD, CADB, CDAB, DABC, DACB, DCAB, n(E) = 12 P(E) = ( ) ( ) = 12 24 = Example 14 What is the probability that she visits (ii) A before B and B before C? S = ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CBAD, CDAB, CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA Let F be the event she visits A before B and B before C F = ABCD, ABDC, ADBC , DABC So, n(F) = 4 P(F) = ( ) ( ) = 4 24 = Example 14 What is the probability that she visits (iii) A first and B last? S = ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CBAD, CDAB, CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA Let G be the event she visits A first and B last G = ACDB, ADCB So, n(G) = 2 P(G) = ( ) ( ) = 2 24 = Example 14 What is the probability that she visits (iv) A either first or second? S = ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CBAD, CDAB, CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA Let H be the event she visits A either first or second H = ABCD, ABDC, ADBC, ACDB, ADBC, ADCB, BACD, BADC,CABD, CADB,DABC, DACB, So, n(H) = 12 P(H) = ( ) ( ) = 12 24 = Example 14 What is the probability that she visits (v) A just before B? S = ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CBAD, CDAB, CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA Let I be the event she visits A just before B I = ABCD, ABDC,CABD,CDAB,DABC,DCAB, So, n(I) = 6 P(I) = ( ) ( ) = 6 24 =