Probability practice · Easy

A man draws a card from a pack of 52 cards and then replaces it. After shuffling the pack, he again draws a card. This he repeats a number of times. The probability that he will draw a heart for the first time in the third draw is

If $X$ is a binomial variate with the range {0,1,2,3,4,5,6} and $P\left( {X = 2} \right) = 4P\left( {X = 4} \right),$ then the parameter $p$ of $X$ is

A letter is taken out at random from `ASSISTANT’ and another is taken out from `STATISTICS’. The probability that they are the same letters is

Five coins are tossed simultaneously. The probability that at least one head turning up, is

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

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

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 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

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

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

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

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

A random variable $X$ takes values 0, 1, 2, 3,… with probability $P\left( {X = x} \right) = k\left( {x + 1} \right){\left( {\frac{1}{5}} \right)^x},$ where $k$ is constant, then $P\left( {X = 0} \right)$ is

If $\mathrm{A}$ and $\mathrm{B}$ are independent events, then which of the following is not true?

If $A$ and $B$ are two mutually exclusive events, then