Probability practice · Mixed difficulty

Four positive integers are taken at random and are multiplied together. Then the probability that the product ends in an odd digit other than 5 is

There are $n$ letters and $n$ addressed envelopes, the probability that all the letters are not kept in the right envelope, is

A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is

The mean and variance of a random variable $X$ having a binomial distribution are 4 and 2 respectively. Then, $P(X > 6)$ is equal to

If $P(A)=0.4, P\left(B^{\prime}\right)=0.6$ and $P(A \cap B)$ $=0.15$ then the value of $P\left(A / A^{\prime} \cup B^{\prime}\right)$ is

A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times, is

If there are 6 girls and 5 boys who sit in a row, then the probability that no two boys sit together is

Two dice are thrown together. Then, the probability that the sum of numbers appearing on them is a prime number, is

Urn $A$ contains 6 red and 4 black balls and urn $B$ contains 4 red and 6 black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is found to be red, is

If a random variable $X$ follows the Binomial distribution $B\left( {33,p} \right)$ such that $3P\left( {X = 0} \right) = P\left( {X = 1} \right),$ then the value of $\frac{{P\left( {X = 15} \right)}}{{P\left( {X = 18} \right)}} - \frac{{P\left( {X = 16} \right)}}{{P\left( {X = 17} \right)}}$ is equal to:

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

If a coin be tossed $n$ times, then probability that the head comes odd times is

A random variable $X$ follows binomial distribution with mean $\alpha$ and variance $\beta$. Then

If $A\;\,\mathrm{and\;}B$ are two mutually exclusive events, then

The mean and standard deviation of a binomial variate $X$ are 4 and $\sqrt 3$ respectively. Then, $P\left( {X \ge 1} \right)$ is equal to

If a random variable $X$ has the following probability distribution values of $X$.
$\begin{array}{cccccccccccccccccccc} {X:}&0&1&2&3&4&5&6&7 \\ {P(X):}&0&k&{2k}&{2k}&{3k}&{{k^2}}&{2{k^2}}&{7{k^2} + k} \end{array}$
Then, $P(X \geq 6)=$

A box contains 2 fifty paise coins, 5 twenty five paise coins and 15 ten paise coins. Five coins are taken out of the box at random. Probability that the value of these five coins is less than one rupee and fifity paise is

A class consists of 100 students, 25 of them are girls and 75 boys, 20 of them are rich and remaining poor, 40 of them are fair complexioned. The Probability of selecting a fair complexioned rich girl is

The probability that a rectangle picked up from a chessboard has the area $6 \mathrm{~cm}^2$ where the distance between consecutive parallel lines on the board is $1 \mathrm{~cm}$, is

Two integers are selected at random from the set {1, 2, …… , 11}. Given that the sum of selected numbers is even, the conditional probability that both the number are even is

If in a trial the probability of success is twice the probability of failure. In six trials the probability of at least four successes is

The probability of obtaining sum ‘8’ in a single throw of two dice is

If three numbers are selected from the set of the first 20 natural numbers, the probability that they are in $G P$, is

In a certain population 10% of the people are rich, 5% are famous and 3% are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to

A person puts three cards addresses to three different people in three envelopes with three different addresses without looking. What is the probability that the cards go into their respective envelopes?

The probability of getting at least one tail in 4 throws of a coin is

From a pack of 52 playing cards, half of the cards are randomly removed without looking at them. From the remaining cards, 3 cards are drawn randomly. The probability that all are king, is :

At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidates who are really capable, $80 \%$ pass the tests and of the incapable, $25 \%$ pass the test. Given that $40 \%$ of the candidates are really capable, then the proportion of capable college students is about

For $n$ independent events ${A'_i}s,\;P\left( {{A_i}} \right) = 1/\left( {1 + i} \right),$ $i = 1,\;2,...,n.$ The probability that atleast one of the events occurs is

The probability that $A$ speaks truth is $\frac{4}{5}\mathrm{\;}$ while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact, is