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

English

Gujarati

Hindi

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 $A$ first and $B$ last ?

Option A

Option B

Option C

Option D

Solution

$S=\left\{\begin{array}{l}A B C D, A B D C, A C B D, A C D B, A D B C, A D C B, \\ B A C D, B A D C, B D A C, B D C A, B C A D, B C D A \\ C A B D, C A D B, C B D A, C B A D, C D A B, C D B A, \\ D A B C, D A C B, D B C A, D B A C, D C A B, D C B A\end{array}\right.$

Let $G$ be the event "she visits $A$ first and $B$ last" $^{\prime \prime}$

$G=\{A C D B, A D C B\}$

So, $n(G)=2$

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

Standard 11

Mathematics

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $

medium

(IIT-2002)

From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is

easy

A card is drawn at random from a well shuffled pack of $52$ cards. The probability of getting a two of heart or diamond is

easy

The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

medium

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ but not $B$

easy

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 ?

Solution

Similar Questions

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $

From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is

A card is drawn at random from a well shuffled pack of $52$ cards. The probability of getting a two of heart or diamond is

The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

Consider the experiment of rolling a die. Let $A$ be the event 'getting a prime number ', $B$ be the event 'getting an odd number '. Write the sets representing the events $A$ but not $B$

Start a Free Trial Now