On her vacations, Veena visits four cities (A, B, C and D) in a

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 Multiple Choice QuestionsLong Answer Type

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481.

On her vacations, Veena visits four cities (A, B, C and D) in a random order. What is the probability that she visits:

(i) A before B? (ii) A before B and B before C?

(iii) A first and B last? (iv) A either first or second (v) A just before B? 


The number of arrangements in which Veena can visit the 4 cities A, B, C, D

                           = straight P presuperscript 4 subscript 4 space equals space 4 factorial space equals space 24

The sample space of the 24 arrangements is:

                       S = open curly brackets table row cell ABCD comma end cell cell ABDC comma end cell cell ACBD comma end cell cell ACDB comma end cell cell ADBC comma end cell cell ADCB semicolon end cell row cell BACD comma end cell cell BADC comma end cell cell BCAD comma end cell cell BCDA comma end cell cell BDAC comma end cell cell BDCA semicolon end cell row cell CABD comma end cell cell CADB comma end cell cell CBAD comma end cell cell CBDA comma end cell cell CDAB comma end cell cell CDBA semicolon end cell row cell DABC comma end cell cell DACB comma end cell cell DBAC comma end cell cell DBCA comma end cell cell DCAB comma end cell DCBA end table close curly brackets

rightwards double arrow                 n(S) = 24

(i) Event E: She visits A before B.
rightwards double arrow                             E = {ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, CABD, CADB, CDAB, DABC, DACB, DCAB}
rightwards double arrow                        n(E) = 12
Hence,                   straight P left parenthesis straight E right parenthesis equals fraction numerator straight n left parenthesis straight E right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 24 equals 1 half

(ii) Event F: Veena visits A before B and B before C.
rightwards double arrow                       F = {ABCD, ABDC, ADBC, DABC}
rightwards double arrow                     n(F) = 4
Hence,       space space straight P left parenthesis straight F right parenthesis equals fraction numerator straight n left parenthesis straight F right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 4 over 24 equals 1 over 6

(iii) Event G: Veena Visits A first and B last
rightwards double arrow                           G = {ACDB, ADCB}
rightwards double arrow                        n(G) = 2
Hence,                  straight P left parenthesis straight G right parenthesis space equals space fraction numerator straight n left parenthesis straight G right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 2 over 24 equals 1 over 12

(iv) Event H: Veena visits A either first or second.
rightwards double arrow                              H = {ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, CABD, CADB, DACB, DABC}
rightwards double arrow                            n(H) = 12
Hence,                    space space straight P left parenthesis straight H right parenthesis space equals space fraction numerator straight n left parenthesis straight H right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 12 over 24 equals 1 half

(v) Event k: Veena visits A just before B.
rightwards double arrow                K = {ABCD, ABDC, CABD, CDAB, DABC, DCAB}
rightwards double arrow             n(K) = 6
Hence,       straight P left parenthesis straight K right parenthesis equals fraction numerator straight n left parenthesis straight K right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 6 over 24 equals 1 fourth
       

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482.

In a relay race, there are five teams, A, B, C, D and E.

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(ii) that A, B and C are first three to finish (in any order)?

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Also, find the probability that the vowels are not all together.

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 Multiple Choice QuestionsLong Answer Type

487. Which of the follwing ‘are’ and ‘are not’ probabilities of occurrence of an event A?
(i) straight P left parenthesis straight A right parenthesis equals 7 over 6                        (ii)  P(A) = 1                       (iii) P(A) = 0
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#6 {main}</pre>
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