Probability practice · Mixed difficulty

For a poisson variate $X,$ if $P\left( {X = 2} \right) = 3P\left( {X = 3} \right),$ then the mean of $X$ is

The letters of word 'SOCIETY' are placed at random in a row. The Probability that three vowels come together, 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 random variable $X$ can attain only the value 1, 2, 3, 4, 5 with respective probabilities $k,2k,3k,2k,k$. If m is the mean of the probability distribution, then $\left( {k,m} \right)$ is equal to

The mean and variance of a random variable $X$ having a binomial distribution are 4 and 2 respectively, then $P(X=1),$ is

$A$ $2 \times 2$ square matrix is written down at random using the numbers $1,-1$ as elements. The probability that the matrix is non-singular is

Seven digits from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are written in a random order. The probability that this seven digit number is divisible by 9 is

Two events $A$ and $B$ have probability 0.25 and 0.50 respectively. The probability that both $A$ and $B$ occur simultaneously is 0.14. Then, the probability that neither $A$ nor $B$ occur, is

A student is given a true-false exam with 10 questions. If he gets 8 or more correct answers he passes the exam. Given that he guesses at the answer to each question, the probability that he passes the exam, is

If $f\left( x \right) = \lambda {e^{ - ax}}(a > 0)$ for $0 \le x < \infty \;$ is a probability density, then $\lambda$ is equal to

Two numbers $x$ and $y$ are chosen at random from the set $\{0,1,2, \ldots, 10\}$. The probability that $|x-y| \leq 5$, is

Four digit numbers are formed using each of the digits 1, 2,..., 8 only once. One number from them is picked up at random. The probability that the selected number contains unity is

In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is

If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before H, H before I and I before S is

If $\frac{{1 + 4\;p}}{p},\frac{{1 - p}}{4},\frac{{1 - 2\;p}}{2}$ are probabilities of three mutually exclusive events, then

Suppose $A$ and $B$ are two events such that $0 < P(B) < 1$. If
$P\left(A \mid B^{\prime}\right)=\frac{P(A)}{1-P(B)}$
then which one of the following is not true?

For a binomial variable $X$ if $n=5$ and $P(X=1)=$ $8 P(X=3)$, then $p$ is given by

$A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ is again chosen at random. The probability that $Q$ is a subset of $P$, is

The coefficients $a,\,b$ and $c$ of the quadratic equation, $a{x^2} + bx + c = 0$ are obtained by throwing a dice three times. The probability that this equation has equal roots is

The Probability of getting the product a perfect square (square of a natural number), when two dice are thrown together, is

Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace is

A is known to tell the truth in 5 cases out of 6 and he states that a white ball was drawn from a bag containing 8 black and 1 white ball. The probability that the white ball was drawn, is

$A$ and $B$ are any two mutally exclusive events, then

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

One ticket is selected at random from 50 tickets numbered 00, 01, 02, …., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero equals

A number $x$ is chosen at random from the set $\{1,2,3, \ldots, 100\}$. Define event: $A=$ the chosen number $x$ satisfies $\frac{x-20}{x-40} \geq 2$. Then $P(A)$ is

From a sales force of 150 persons, one will be selected to attend a special sales meeting. If 52 of them are unmarried, 72 are college graduates, and $\frac{3}{4}$ of the 52 that are un married are college graduates, the probability that a sales person selected at random will be neither single nor a college graduate, is

A biased coin with probability $p,\;0 < p < 1$ of heads is tossed until a head appears for the first time. If the probability that the number of tossed required is even is $\frac{2}{5},\;$ then $p\;$ equals

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

Consider 5 independent Bernoulli's trials each with probability of success $P$. If the probability of atleast one failure is greater than or equal to $\frac{31}{32}$, then $P$ lies in the interval