Probability practice · Mixed difficulty

Two events $E$ and $F$ are independent. If $P(E)=0.3$, $P(E \cup F)=0.5$, then $P(E \mid F)-P(F \mid E)$ equals

The probability that a randomly chosen one-one function from the set $\{a, b, c, d\}$ to the set $\{1,2,3$, $4,5\}$ satisfies $f(a)+2 f(b)-f(c)=f(d)$ is :

A dice is thrown 100 times, getting an even number is considered a success. The variance of the number of successes is

A box contains 10 good articles and 6 with defects, one article is chosen at random. What is the probability that it is either good or has a defect?

Consider the polynomial $P(x)=x^3+a x^2+b x+c$ where $a, b, c \in\{1,2, \ldots \ldots . ., 10\}$ then the probability that $P(x)$ is divisible by $x^2+x+1$ is

Unbiased die is thrown, probability that outcome is greater than 4, is

Four persons $A, B, C, D$ are to speak at a function along with 6 others. If they all speak in random order, the probability that $A$ speaks before $B, B$ before $C, C$ before $D$ is

If the probability that $A$ and $B$ will die with in a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is

Let $A$ and $B$ be two independent events such that $P\left( A \right) = \frac{1}{3}$ and $P\left( B \right) = \frac{1}{6}.$ Then, which of the following is TRUE?

An unbiased coin is tossed fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads is

A sample space consists of 3 sample points with associated probabilities given as $2 p, p^2, 4 p-1$. Then the value of $p$ is -

Three numbers are chosen at random from the numbers $1,2, \ldots 20$. The probability that the arithmetic mean of these numbers is 4 is

The probability of event $A$ occurring is $0.5$ and B occurring is 0.3. If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ occurring is

Three persons $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $\mathrm{P}$ or $\mathrm{Q}$ but not by $\mathrm{R}$ is :

Two cards are drawn one by one at random from a pack of 52 cards. The prohahility that both of them are king, is

Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a coloured one is (before drawing second card first card is not placed again in the pack)

A fair coin is tossed repeatedly until a head is obtained. If $\mathrm{X}$ denotes the number of tosses required, then the conditional probability of $X \geq 6$, given that $X>3$ is

Three numbers are chosen from 1 to 30. The probability that they are not consecutive is

In a class of 80 students numbered 1 to 80 , all odd numbered students opt of Cricket, students whose numbers are divisible by 5 opt for Football and those whose numbers are divisible by 7 opt for Hockey. If the number of students who do not opt any of the three games is $n$, then $\frac{n}{4}$ is equal to

Three numbers are chosen at random from numbers 1 to 30 . The probability that the minimum of the chosen numbers is 9 and maximum is 25 , is

Two squares are chosen at random on a chessboard. If $p$ denotes the probability that they have exactly one side in common, then $144 p$ is

A group consists $2 n$ students including you and your friend. If the group is split into two different sections $A$ and $B$, each containing $n$ students, then the probability that you and your friend are in the different sections is

If $A=\{x: x=4 n+1, n \leq 5, n \in N\}$ and $B\{3 n: n \leq 8$, $n \in N\}$, then find $(A-(A-B))$.

10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the some boy does not receive both the pens is

A five digit mumber is formed by the digits 1, 2, 3, 4, 5,6 and 8. The probability that the number has even digit at both ends is

Events $A, B, C$ are mutually exclusive events such that $P(A)=\frac{3 x+1}{3}, P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2 x}{2}$. The set of all possible values of $x$ are in the interval

One hundred identical coins, each with probability $p$ of showing heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of $p$, is

A random variable $X$ has poisson distribution with mean 2. Then, $P(X > 1.5)$ equals

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is:

A number is chosen form each of two sets $A=\{1,2,3,4,5,6,7,8\}$ and $B=\{8,7,6,5,4,3,2,1\}$.
If $p_1$ is the probability that the sum of the numbers is 9 and $p_2$ is the probability that sum of the numbers is 7 , then $p_1+p_2$ is equal to