Probability practice · Mixed difficulty

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of the experiment, is

There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there after a ball is drawn at random from the urn, then the probability that it is white is

The mean and variance of binomial distribution are 4 and 3 respectively. Then, the probability of getting exactly six success in this distribution is

When three dice are thrown the probability of getting 4 or 5 on each of the dice simultaneously, is

There is an objective type question with 4 answer choices exactly one of which is correct. A student has not studied the topic on which the question has been set. The probability that the student guesses the correct answer, is

If $A$ and $B$ are independent events such that $P(B)=\frac{2}{7}, P(A \cup \bar{B})=0.8$, then $P(A)=$

A six faced fair die is thrown until 1 comes. Then, the probability that 1 comes in even number of trials, is

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

A coin is tossed three times is succession. If $\mathrm{E}$ is the event that there are at least two heads and $\mathrm{F}$ is the event in which first throw is a head, then $\mathrm{P}(\mathrm{E} / \mathrm{F})$ equal to:

In shuffling a pack of playing cards, four are accidently dropped. The probability that missing cards should be one from each suit, is

A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring their roots. The chance that the chosen equation has equal roots, is

The probability that two randomly selected subsets of the set $\left\{ {1,2,3,4,5} \right\}$ have exactly two elements in their intersection, is

Suppose $n$ students appear in an examination. Let $X=$ the number of students who pass the examination. Suppose $P(X=k)=\lambda k^2$, then value of $\lambda$ is

The probability of forming a three digit numbers with the same digits when three digit numbers are formed out of the digit 0, 2, 4, 6, 8 is

If $A$ and $B$ are events of a random experiment such that $P\left( {A \cup B} \right) = \frac{4}{5},P\left( {\bar A \cup \bar B} \right) = \frac{7}{{10}}$ and $P\left( B \right) = \frac{2}{5}$ then $P\left( A \right)$ equals

A bag $A$ contains 4 green and 3 red balls and bag $B$ contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted to be green. The probability that it comes from bag $B$, is

The probability of having at least one tail in 4 throws with a coin, is

Five persons $A,\,\;B,\,\;C,\;\,D$ and $E$ are in queue of a shop. The probability that $A$ and $E$ always together, is

Suppose $n(\geq 3)$ persons are arranged in a row. The probability that two particular persons are not together is

An article manufactured by a company consits of two parts $A$ and $B$. In the processs of manufacutre of part $A$, 9 out of 100 are likely to be defective. Similarly 5 out of 100 are likely to be defective in the manufacture of part $B$. The probability that the assembled part will not be defective, is

The mean and variance of 5 observations of an experiment are 4 and 5.2 respectively. If from these observations three are 1,2 and 6 , then the mean of remaining will be-

If a triangle is formed by choosing the vertices of 10 sided regular polygon. Then probability that triangle has exactly one side in common with the polygon, is

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required. The probability that $X \geq 3$ equals

A rifleman is firing at a distant target and has only $10 \%$ chance of hitting it. The least number of rounds, he must fire in order to have more than $50 \%$ chance of hitting it at least once, is

Two different families $A$ and $B$ are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket.
If the probability that all the tickets go to the children of the family $B$ is $\frac{1}{12}$, then the number of children in each family is?

A fair die is rolled. The probability that the first time 1 occurs at the even throw is

If $A$ and $B$ are two independent events such that $P(\bar{B})=\alpha P(\bar{A})=\frac{7}{10}, P(\bar{B})=\alpha$ and $P(A \cup B)=\frac{8}{10}$, then $\alpha$, is

The probability of a man hitting a target is $\frac{2}{5}$. He fires at the target $k$ times ( $k$, a given number). Then the minimum $k$, so that the probability of hitting the target at least once is more than $\frac{7}{10}$, is :

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T- shirt is

Let $A, B, C$ be pairwise independent events with $P(C)>0$ and $P(A \cap B \cap C)=0$. Then, $P\left(A^c \cap B^c / C\right)$ is equal to