Example 14 - On her vacations Veena visits four cities A, B, C, D

Example 14 - Chapter 16 Class 11 Probability - Part 2
Example 14 - Chapter 16 Class 11 Probability - Part 3 Example 14 - Chapter 16 Class 11 Probability - Part 4 Example 14 - Chapter 16 Class 11 Probability - Part 5 Example 14 - Chapter 16 Class 11 Probability - Part 6

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Example 9 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 = {β–ˆ("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 β€œshe visits A before Bβ€œ Hence , E = {β–ˆ("ABCD, ABDC, ADBC, ACDB, ADBC, ADCB," @"CABD, CADB, CDAB, " @"DABC, DACB, DCAB," )} n(E) = 12 P(E) = (𝑛(𝐸))/(𝑛(𝑆)) = 12/24 = 𝟏/𝟐 Example 14 What is the probability that she visits (ii) A before B and B before C? S = {β–ˆ("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 β€œshe visits A before B and B before C β€œ F = {β–ˆ("ABCD, ABDC, ADBC , DABC" )} So, n(F) = 4 P(F) = (𝑛(𝐹))/(𝑛(𝑆)) = 4/24 = 𝟏/πŸ” Example 14 What is the probability that she visits (iii) A first and B last? S = {β–ˆ("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 β€œshe visits A first and B last” G = {β–ˆ("ACDB, ADCB" )} So, n(G) = 2 P(G) = (𝑛(𝐺))/(𝑛(𝑆)) = 2/24 = 𝟏/𝟏𝟐 Example 14 What is the probability that she visits (iv) A either first or second? S = {β–ˆ("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 β€œshe visits A either first or second” H = {β–ˆ("ABCD, ABDC, ADBC, ACDB, ADBC, ADCB," @" BACD, BADC,CABD, CADB,DABC, DACB," )} So, n(H) = 12 P(H) = (𝑛(𝐻))/(𝑛(𝑆)) = 12/24 = 𝟏/𝟐 Example 14 What is the probability that she visits (v) A just before B? S = {β–ˆ("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 β€œshe visits A just before B” I = {β–ˆ("ABCD, ABDC, CABD, CDAB, DABC, DCAB," )} So, n(I) = 6 P(I) = (𝑛(𝐼))/(𝑛(𝑆)) = 6/24 = 𝟏/πŸ’

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.