Probability practice · Easy

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is 1/n. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is:

Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}(n, 2022)=1$, is

A student takes his examination in four subjects $\alpha, \beta$, $\gamma, \delta$. He estimates his chance of passing in $\alpha$ as $\frac{4}{5}$, in $\beta$ as $\frac{3}{4}$, in $\gamma$ as $\frac{5}{6}$ and in $\delta$ as $\frac{2}{3}$. To qualify he must pass in $\alpha$ and at least two other subjects. The Probability that he qualifies 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

If $m$ rupee coins and $n$ ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins, is

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

Let ${E_1},{E_2}$ be two mutually exclusive events of an experiment with $P$(not ${E_2}$) $= 0.6 = P\left( {{E_1} \cup {E_2}} \right)$.Then, $P\left( {{E_1}} \right)$ is equal to

A four digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is

Assertion: Probability of getting a head in a toss of an unbiased coin is $\frac{1}{2}$.

Reason: In a simultaneous toss of two coins, the probability of getting 'no tails' is $\frac{1}{4}$.

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $1/6$ and the probability that neither of them occurs is $1/3$. Then,

A bag contains 16 coins of which two are counterfeit with heads on both sides. The rest are fair coins. One is selected at random from the bag and tossed. The probability of getting a head is

If $A$ and $B$ are independent events of $a$ random experiment such that $P(A \cap B)=\frac{1}{6}$ and $P(\bar{A} \cap \bar{B})=\frac{1}{3}$, then $P(A)$ is equal to

A bag $X$ contains 2 white and 3 black balls and another bag $Y$ contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, probability for the ball chosen be white, is

On each evening a boy either watches DOORDARSHAN channel or TENSPORTS. The probability that he watches TEN SPORTS is $\frac{4}{5}$. If he watches DOORDARSHAN, there is a chance of $\frac{3}{4}$ that he will be asleep, while it is $\frac{1}{4}$ when he watches TEN SPORTS. On one day, the boy is found to be asleep. The probability that the boy watched DOORDARSHAN is

Five different objects ${A_1},\,{A_2},\,{A_3},\,{A_4},\,{A_5}$ are distributed randomly in 5 places marked 1, 2, 3, 4, 5. One arrangement is picked at random. The probability that in the selected arrangement, none of the object occupies the place corresponding to its number, is

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

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