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

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14.Probability

medium

On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ either first or second?

Option A

Option B

Option C

Option D

Solution

$S=\left\{\begin{array}{l} ABCD , ABDC , ACBD , ACDB , ADBC , ADCB , \\ BACD , BADC , BDAC , BDCA , BCAD , BCDA \\ CABD , CADB , CBDA , CBAD , CDAB , CDBA , \\ DABC , DACB , DBCA , DBAC , DCAB , DCBA \end{array}\right.$

Let $H$ be the event "she visits A either first or second"

$H=\left\{\begin{array}{r} ABCD , ABDC , ADBC , ACDB , ADBC , ADCB , \\ BACD , BADC , CABD , CADB , DABC , DACB ,\end{array}\right\}$

$So , n ( H )=12$

$P(H)=\frac{n(H)}{n(S)}$ $=\frac{12}{24}=\frac{1}{2}$

Standard 11

Mathematics

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(KVPY-2014)

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Solution

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