(B) Let $A$ and $B$ select numbers $x$ and $y$ respectively from the set $\{1, 2, 3, \ldots, n\}$. The total number of possible outcomes is $n \times

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(B) Let $A$ and $B$ select numbers $x$ and $y$ respectively from the set $\{1, 2, 3, \ldots, n\}$. The total number of possible outcomes is $n \times n = n^2$.The number of ways such that $x Given the probability $P(x Solving for $n$: $2019(n-1) = 2018n \Rightarrow 2019n - 2019 = 2018n \Rightarrow n = 2019$.Now,we need the probability that $y = x + 1$. The possible pairs $(x, y)$ such that $y = x + 1$ are $(1, 2), (2, 3), \ldots, (n-1, n)$. There are $n-1$ such pairs.Thus,the required probability is $\frac{n-1}{n^2} = \frac{2019-1}{(2019)^2} = \frac{2018}{(2019)^2}$.

Class 12 Mathematics Probability Mix Examples-Probability

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$A$ and $B$ each select one number at random from the distinct numbers $1, 2, 3, \ldots, n$. The probability that the number selected by $A$ is less than the number selected by $B$ is $\frac{1009}{2019}$. The probability that the number selected by $B$ is the number immediately next to the number selected by $A$ is:

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A
$\frac{2018}{2019}$
B
$\frac{2018}{(2019)^2}$
C
$\frac{2000}{2019}$
D
$\frac{2000}{(2019)^2}$

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Cards are drawn one after the other without replacement from a well-shuffled pack of cards until an ace card appears. If the probability that exactly $5$ cards are drawn before the first ace card appears is $\frac{4}{49}\left(\frac{p_1 \cdot p_2 \cdot p_3}{p_4 \cdot p_5 \cdot p_6}\right)$, where $p_i$ is prime for $i=1, 2, 3, 4, 5, 6$, then $(\max \{p_i\} - \min \{p_i\}) = $

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There are $3$ houses available in a residential area. $3$ people apply for the houses. If each person applies for a house without consulting others,what is the probability that all $3$ apply for the same house (in $/9$)?

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If a man throws a die until he gets a number bigger than $3$, then the probability that he gets a $5$ in his last throw is

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If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B)=\frac{1}{6}$ and $P(\bar{A} \cap \bar{B})=\frac{1}{3}$, then $P(A)$ is equal to (Here, $\bar{E}$ is the complement of the event $E$)

MediumTS EAMCET 2008

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Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that the minimum of the two numbers is divisible by $3$ or the maximum of the two numbers is divisible by $4$ is:

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There are $3$ houses available in a residential area. $3$ people apply for the houses. If each person applies for a house without consulting others,what is the probability that all $3$ apply for the same house (in $/9$)?

If a man throws a die until he gets a number bigger than $3$, then the probability that he gets a $5$ in his last throw is

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