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A fourdigit number is formed by the digits \( 1, 2, 3, 4 \) with no repetition. The probability that the number is odd is _________.
Required probability
If the integers \( m\ \text{ and }\ n \) are chosen at random from \( 1\ \text{ to }\ 100 \), then the probability that a number of the form \( 7^n+7^m \) is divisible by \( 5 \) equals _________.
Number of favourable ordered pair
Sample space (S)
One mapping is selected at random from all the mappings of set \( \text{A}=\left\{ 1, 2, 3,…,n \right\} \) into itself. The probability that the mapping selected is oneone is _________.
Total number of mappings from
Total number of oneone mapping
Three of six vertices of a regular hexagon are chosen at random.
The probability that the triangle with three vertices is equilateral is _________.
If three squares are chosen on a chess board, the chance that they should be in a diagonal line is _________.
In a class, there are \( 10 \) boys and \( 8\) girls. When \( 3 \) students are selected at random the probability that \(2 \) girls and \(1 \) boy are selected is _________.
From a group of \( 8 \) boys and \( 3 \)girls, a committee of \( 5 \) members are to be formed.
Find the probability that \( 2 \) particular girls are included in the committee.
The probability that the three cards drawn from a pack of \( 52 \) cards, are all black is ________.
cards are black out of .
A determinant of second order is made with the elements \( 0\text{ and }1 \),
What is the probability that the determinant is positive?
Total number of ways .
The favorable ways are
The probability of choosing randomly a number \( C \) from the set \( \left\{ 1,2,3,…,9 \right\} \) such that the quadratic equation \( x^2+4x+c=0 \) has real roots, is _________.
A letter is taken out at random from ‘ASSISTANT’ and another is taken out from ‘STATISTICS’.
The probability that they are the same letter is _________.
A coin is tossed thrice. The probability of getting a head once and a tail twice is _________.
If \( A \) and \( B \) are two events with \( P(A^\prime)=0.3,\ P(B)=0.4 \) and \(P(A\cap B^c)=0.5 \). Then \( P\left[ \dfrac{B}{(A\cup B^c)} \right] \) _________.
If \( n \) positive integers are taken at random and multiplied together, then the probability that the last digit of the product is \( 2,4,6\text{ or }8 \) is _________.
\( \text{Let}\ A, B,\text{and }C \) be the three events such that \( P(A)=0.3,\ P(B)=0.4,\ P(A\cap B)=0.08 P(A\cap C)=0.28 \) and \( P (A\cap B\cap C)=0.09 \). If \( P(A\cup B\cup C)\geq 0.75 \) ,then [ mathjax]\(P(B\cap C) \)_________.
If \( A\text{ and } B \) are two events of a random experiment such that \( P(A\cup B)=\dfrac{4}{5},\ P(A^\prime\cup B^\prime)=\dfrac{7}{10}\ \text{ and }P(B)=\dfrac{2}{5} \), then the value of \( P (A) \) is equal to ___________.
If \( A\text{ and } B \) are two events of a random experiment such that \( P(A\cup B)=\dfrac{4}{5},\ P(A^\prime\cup B^\prime)=\dfrac{7}{10}\ \text{ and }P(B)=\dfrac{2}{5} \), then the value of \( P (A) \) is equal to ___________.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that is a vowel is _________.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that is a vowel is _________.
Three houses are available in a locality. Three persons apply for the houses.
Each applies for one house without consulting others. The probability that all the three apply for the same house is _________.
Three houses are available in a locality. Three persons apply for the houses.
Each applies for one house without consulting others. The probability that all the three apply for the same house is _________.
A committee of five is to be chosen from a group of \( 9 \) people.The probability that a certain married couple will either serve together or not at all is _________.
A committee of five is to be chosen from a group of \( 9 \) people.The probability that a certain married couple will either serve together or not at all is _________.
A fair dice is tossed eight times. The probability that a third six is observed on the eight throw is _________.
A fair dice is tossed eight times. The probability that a third six is observed on the eight throw is _________.
If a number \( ‘n’ \) is chosen at random from set \( \left\{ 1, 2, 3,…,1000 \right\} \). Then the probability that is a number that leaves remainder \( 1 \),when divided by \( 7 \) is _________.
If a number \( ‘n’ \) is chosen at random from set \( \left\{ 1, 2, 3,…,1000 \right\} \). Then the probability that is a number that leaves remainder \( 1 \),when divided by \( 7 \) is _________.
The probability that a number \( ‘n’ \) choosen at random from \( 1 \) to \( 30 \) , to satisfy \( n+\dfrac{50}{n} \) > \(27 \) is _________.
The probability that a number \( ‘n’ \) choosen at random from \( 1 \) to \( 30 \) , to satisfy \( n+\dfrac{50}{n} \) > \(27 \) is _________.
If three coins are tossed, then what is the probability that atleast two heads appears on upper face?
If three coins are tossed, then what is the probability that atleast two heads appears on upper face?
A number \( n \) is choosen at random from \( S= \{1,2,…,50\} \). Let \(A=\left\{ n \in S : n +\dfrac{50}{n} > 27 \right\}, B =\left\{ n \in S: n \text { is a prime} \right\} \) and \( C=\left\{ n \in S : n \text{ is a square} \right\} \) thne, a correct order of their probability is_____
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A number \( n \) is choosen at random from \( S= \{1,2,…,50\} \). Let \(A=\left\{ n \in S : n +\dfrac{50}{n} > 27 \right\}, B =\left\{ n \in S: n \text { is a prime} \right\} \) and \( C=\left\{ n \in S : n \text{ is a square} \right\} \) thne, a correct order of their probability is_____
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If events \( A, B \) are independent, \(P(A^c)=\dfrac{2}{3} \), \( P(B^c)=\dfrac{2}{7} \) then \( P (A\cap B) \) is equal to_________.
If events \( A, B \) are independent, \(P(A^c)=\dfrac{2}{3} \), \( P(B^c)=\dfrac{2}{7} \) then \( P (A\cap B) \) is equal to_________.