Probability practice · Mixed difficulty

A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the
locker by dialing three digits at random. The probability that the stranger succeeds at the $k^{\text {th }}$ trial is

Three natural numbers are taken at random from the set of first 100 natural numbers. The probability that their A.M. is 25, is

A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw, is

A six faced die is a biased one. It is thrice more likely to show an odd number than show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is

An urn contains five balls. Two balls are drawn and are found to be white. The probability that the balls selected are white is

If the mean and standard deviation of a binomial distribution are 12 and 2 respectively, then value of its parameter $p$ is

If ${A_1},{A_2}, \ldots ,{A_n}$ are $n$ independent events such that $P\left( {{A_i}} \right) = \frac{1}{{i + 1}},i = 1,2, \ldots ,n.$ The probability that none of the $n$ events occurs, is

Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is

An unbiased coin is tossed $n$ times. Let $X$ denote the number of times head occurs. If $P\left( {X = 4} \right),P\left( {X = 5} \right)$ and $P\left( {X = 6} \right)$ are in AP, then the value of $n$ can be

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

Among the workers in a factory only 30% receive bonus and among those receiving bonus only 20% are skilled. The probability that a randomly selected worker is skilled and is receiving bonus is

If six students, including two particular students $A$ and $B$, stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is

A dice is thrown $(2 n+1)$ times. The probability that faces with even numbers show odd number of times is

Let $A, B$ and $C$ are pairwise independent events with $P(C)>0$ and $P(A \cap B \cap C)=0$. Then, $P\left(\frac{\left(A^c \cap B^c\right)}{C}\right)$ is

In a college, $30 \%$ students fail in physics, $25 \%$ fail in Mathematics and $10 \%$ fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in mathematics, is

The probability that $A$ can solve a problem is 2/3 and $B$ can solve it is 3/4. If both attempt the problem, what is the probability that the problem gets solved?

If $A$ and $B$ are events of the same experiments with $P\left( A \right) = 0.2,\;P\left( B \right) = 0.5$, then maximum value of $P\left( {A' \cap B} \right)$ is

If $P(A \cap B)=1 / 2, P\left(A^{\prime} \cap B^{\prime}\right)=1 / 3, P(A)=p$ and $P(B)=2 p$ then value of $p$ is

In a test an examinee either guesses, copies or knows the answer to multiple choice question with five choices. The probability that he makes a guess is $\frac{1}{4}$ and probability that he copies the answer is $\frac{1}{8}$. The probability that his answer is correct given that he copies is $\frac{1}{10}$. Find the probability that he knows the answer to the question given that he correctly answered it:

A bag contains four tickets marked with numbers 112, 121, 211, 222. One ticket is drawn at random from the bag. Let ${E_i}\left( {i = 1,\,2,\,3} \right)$ denote the event that ith digit on the ticket is 2. Then, which one of the following is incorrect?

Three dice are thrown simultaneously, then probability of throwing a total greater than 4 is

In tossing of a coin $\left( {m + n} \right)(m > n)$ times, the probability of coming consecutive heads at least $m$ times is

Five numbers, ${x_1},{x_2},{x_3},{x_4},{x_5}$ are randomly selected from the numbers 1, 2, 3,….., 18 and are arranged in the increasing order $({x_1} < {x_2} < {x_3} < {x_4} < {x_5}).$ The probability that ${x_2} = 7$ and ${x_4} = 11$ is:

If $X$ and $Y$ are independent binomial variates $B(5,1 / 2)$ and $B(7,1 / 2)$ then $P(X+Y)=3$, is

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

Suppose $E$ and $F$ are two independent events of a random experiment. If the probability of occurrence of $E$ is $\frac{1}{5}$ and the probability of occurrence of $F$ given $E$ is $\frac{1}{{10}}$,then the probability of non-occurrence of at least one of the events $E$ and $F$ is

n biscuits are distributed among $N$ beggars at random. The probability that a particular beggar gets $r\left( {\, < n} \right)$ biscuits, is

Two numbers are chosen, one by one (without replacement) from the set of numbers ${A}=\{1,2,3,4,5,6\}$. Then the probability that minimum value of two numbers chosen is less than 4 , is:

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6) and let ${E_k} = \left\{ {\left( {a,\;b} \right) \in S:ab = k} \right\}\;$ for $k \ge 1.$
If ${p_k} = P\left( {{E_k}} \right)$ for $k \ge 1,\;$ then the correct among the following, is