On her vacations,Veena visits four cities (A, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The total number of ways to arrange the four cities $A, B, C$,and $D$ is $4! = 24$. Thus,the total number of outcomes in the sample space is $n(S)

Vedclass · Accepted Answer

$1/6$

Vedclass · Answer

(A) The total number of ways to arrange the four cities $A, B, C$,and $D$ is $4! = 24$. Thus,the total number of outcomes in the sample space is $n(S) = 24$.We are interested in the event $F$ where Veena visits $A$ before $B$ and $B$ before $C$. This means the relative order of $A, B$,and $C$ must be $A 	o B 	o C$.In any permutation of the four cities,there are $3! = 6$ possible relative orders for the cities $A, B$,and $C$. These are:$(A, B, C), (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, B, A)$.Only one of these orders,$(A, B, C)$,satisfies the condition that $A$ comes before $B$ and $B$ comes before $C$.Since each of these $6$ relative orders is equally likely to occur in the total $24$ permutations,the probability is $\frac{1}{6}$.

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 $B$ and $B$ before $C$?

Similar Questions

$A$ class has $15$ boys and $5$ girls. Suppose $3$ students are selected at random from the class. The probability that there are $2$ boys and $1$ girl is

Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of hearts.

$A$ bag contains $3$ red and $3$ white balls. If two balls are drawn one after another,what is the probability that they are of different colors?

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

If out of $20$ consecutive whole numbers two are chosen at random,then the probability that their sum is odd,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module