Probability practice · Mixed difficulty

In a multiple choice question, there are five alternative answers of which one or more than one are correct. A candidate will get marks on the question, if he ticks all the correct answers. If he decides to tick answers at random, then the least number of choice should he be allowed so that the probability of his getting marks on the question exceeds $\frac{1}{8}$ is

Three persons $A, B$ and $C$ are to speak at a function along with five others. If they all speak in random order, the probability that $A$ speaks before $B$ and $B$ speaks before $\mathrm{C}$ is

An ordinary cube has four blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 9 in 5 throws, is

There are 4 white and 4 black balls in a bag and 3 balls are drawn at random. If balls of same colour are identical, the probability that none of them is black, is

There are 4 white and 3 black balls in a box. In another box there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3 then a ball is drawn from the first box but if it shows a number more than 3 then a ball is drawn from the second box. If the ball drawn is black then the probability that the ball was drawn from the first box is

Two numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 100$ and are multiplied. Then, the probability that the product $a b$ is divisible by 3 , is

Let $A$ and $B$ be independent events such that $P(A) = p$ and $P(B) = 2p$. The largest value of $p$, for which $P$ (exactly one of $A$, $B$ occurs) $\frac{5}{9}$, is

Three numbers are chosen at random without replacement from $\{1,2,3, \ldots, 8\}$. The probability that their minimum is 3 , given that their maximum is 6 , is

A wire of length $l$ is cut into three pieces. What is the probability that the three pieces from a triangle?

Refer to question 19 above. If the probability that exactly two of the three balls were red, then the first ball being red, is

If $A_1, A_2, \ldots, A_n$ are any $n$ events, then

If $X$ has binomial distribution with mean $np$ and variance $npq,$ then $\frac{{P\left( {X = k} \right)}}{{P\left( {X = k - 1} \right)}}$ is equal to

If 15 boys of different ages are distributed into 3 groups of 4, 5, and 6 boys randomly then the probability that three youngest boys are in different groups is

A book writer writes a good book with probability $\frac{1}{2}$. If it is a good book, the probability that it will be published is $\frac{2}{3}$, otherwise it is $\frac{1}{4}$. If he writes 2 books, the probability that at least one book will be published is

Probability $P\left( A \right) = \frac{4}{5},P\left( {B'} \right) = \frac{2}{5}$ and $P\left( {A \cap B} \right) = \frac{1}{2},$ then $P\left( {A \cap B'} \right)$ is equal to

The probabilities of three events $A, B$ and $C$ are given $P(A)=0.6, P(B)=0.4$ and $P(C)=0.5$. If $P(A \cup B)=0.8$, $P(A \cap C)=0.3, \quad P(A \cap B \cap C)=0.2, \quad P(B \cap C)=\beta \quad$ and $P(A \cup B \cup C)=\alpha$, where $0.85 \leq \alpha \leq 0.95$, then $\beta$ lies in the interval

Probability that A speaks truth is $4 / 5$. A coin is tossed. A reports that a head appears. The probability that actually there was head is

Numbers are selected at random one at a time, from the numbers $00,01,02, \ldots, 99$ with replacement. An event $E$ occurs if and only if the product of the two digits of a selected number is 18 . If four numbers are selected, then the probability that ${E}$ occurs at least 3 times, is

A coin is tossed 10 times. The probability of getting exactly six heads, is

A random variable $X$ takes the values $0,1,2,3$ and its mean is 1.3. If $P(X=3)=2 P(X=1)$ and $P(X=2)=0.3,$ then $P(X=0),$ is

Let $A=\{1,2,3,4\}$ and $B=\{a, b\}$. A function $f: A \rightarrow B$ is selected randomly. Probability that function is an onto function is

If $P\left( {A \cup B} \right) = 0.8$ and $P\left( {A \cap B} \right) = 0.3,$ then $P\left( {A'} \right) + P\left( {B'} \right)$ equals to

A coin is tossed and a die is rolled. The probability that the coin shows the head and the die shows 6 is

A coin is tossed $n$ times. The probability of getting head at least once is greater than 0.8, then the least value of $n$ is

In a simultaneous throw of three coins, what is the probability of getting at least 2 tails

In an entrance test there are multiple choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is 90%. If be gets the correct answer to a question, then the probability that he was guessing, is

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2, \sqrt{3 N}, N+2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is

A person throws two dice, one the common cube and the other regular tetrahedron with numbers $1,2,3,4$ on its faces, the number on the lowest face being taken in the case of a tetrahedron. The chance that the sum of numbers thrown is not less than 5 is

If two events are independent, then

Out of $3n$ consecutive natural numbers, 3 natural numbers are chosen at random without replacement. The probability that the sum of the chosen numbers is divisible by 3, is