Probability practice · Easy

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 $P(A \cap B)=1 / 2, P\left(A^{\prime} \cap B^{\prime}\right)=1 / 3, P(A)=p$ 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:

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

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:

If eight coins are tossed together, then the probability of getting exactly 3 heads is

Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another

If the mean and S.D. of a binomial distribution are 20 and 4 respectively, then the number of trials is

If $P(A)=\frac{4}{5}$ and $P(A \cap B)=\frac{7}{10}$, then $P(B / A)$ is equal to

Two numbers are selected at random from set of the first 100 natural numbers. The probability that the product obtained is divisible by 3 is $\mathrm{k}$ then $\frac{150 \mathrm{k}}{83}$ is equal to

If $E$ and $F$ are two events such that $0 < P(F) < 1$, then

If the mean and variance of a binomial distribution are 4 and 3 respectively, then $P(X=1)$ is

A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of percolator coffee $75 \%$ of time. It is agreed that his claim will be accepted if he correctly identifies at least 5 of the 6 cups. His chances of having the claim accepted is

If $A=\{2,3,4,8,10\}, B=\{3,4,5,10,12\}, C=\{4,5, 6,12,14\}$ then find $(A \cap B) \cup(A \cap C)$.

The numbers $1,2,3, \ldots, n$ are arranged in a random order. Then, the probability that the digits $1,2,3, \ldots ,k(k < n)$ appears as neighbours, is

A box contains 100 bulbs out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective, is

Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If $P(T)$ denotes the probability of occurrence of the event $T$, then

Three different numbers are selected at random from the set $A=\{1,2, \ldots, 10\}$. The probability that the product of two of the numbers is equal to third is

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95