Probability practice · Easy

A fair die is tossed eight times. The probability that a third six is observed in the eight throw is

A bag contains 5 blue balls and unknown numbers of red balls, two balls are drawn at random. The probability of both of them are blue is $\frac{5}{{14}}$, then the number of red balls are

The probability of India winning a test match against England is $\frac{2}{3}.$ Assuming independence from match to match, the probability that in a 7 match series India's third win occurs at the fifth match, is

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is

The probability that the same number appear on throwing three dice simultaneously, is

There are 5 duplicate and 10 original items in an automobile shop and 3 items are brought at random by a customer. The probability that none of the items is duplicate, is

For a poisson variate $X,$ if $P\left( {X = 2} \right) = 3P\left( {X = 3} \right),$ then the mean of $X$ 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 $\frac{{1 + 4\;p}}{p},\frac{{1 - p}}{4},\frac{{1 - 2\;p}}{2}$ are probabilities of three mutually exclusive events, then

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

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

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

A die is thrown. If it shows a six, we draw a ball from a bag consisting 2 black balls and 6 white balls. If it does not show a six, then we toss a coin. Then, the sample space of this experiment consists of

Two non-negative integers are chosen at random. The probability that the sum of the square is divisible by 5 is