On her vacations Veena visits four cities $( A ,\, B ,\, C$ and $D )$ in a random order. What is the probability that she visits $A$ just before $B$ ?
On her vacations Veena visits four cities $( A ,\, B ,\, C$ and $D )$ in a random order. What is the probability that she visits $A$ just before $B$ ?
$S=\left\{\begin{array}{l}A B C D, A B D C, A C B D, A C D B, A D B C, A D C B \\ B A C D, B A D C, B D A C, B D C A, B C A D, B C D A \\ C A B D, C A D B, C B D A, C B A D, C D A B, C D B A, \\ D A B C, D A C B, D B C A, D B A C, D C A B, D C B A\end{array}\right.$
Let I be the event "she visits A just before B"
$I =\{ ABCD , ABDC , CABD , CDAB , DABC , DCAB ,\}$
$So , n ( I )=6$
$P(I)=\frac{n(I)}{n(S)}$ $=\frac{6}{24}=\frac{1}{4}$
Similar Questions
Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
Describe the events $A^{\prime }.$
Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
Describe the events $A^{\prime }.$
An experiment consists of recording boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ?
An experiment consists of recording boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ?
The probability of getting a number greater than $2$ in throwing a die is
The probability of getting a number greater than $2$ in throwing a die is
A locker can be opened by dialing a fixed three digit code (between $000$ and $999$). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the ${k^{th}}$ trial is
A locker can be opened by dialing a fixed three digit code (between $000$ and $999$). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the ${k^{th}}$ trial is
A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is
A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is