Probability PYQs - Last 10 Years

An engineering team is testing a new prototype drone. The drone has constant success rate of $\frac{\mathbf{2}}{\mathbf{7}}$ for every autonomous landing attempt. Two engineers, Sarah and Swarna, take turns initiating the landing sequence, ...

Samhita faces a three-headed dragon. She wins a "Tactical medal" if she manages to defeat exactly one of the three heads.
The battle proceeds head-by-head under the following conditions:

The probability of defeating the first head is $\fra...

A teacher has two jars of candy on her desk:
Jar 1: Contains 3 Strawberry candies and 2 Orange candies.
Jar 2: Contains 1 Strawberry candy and 4 Orange candies.
The teacher randomly picks two candies from Jar 1 and drops them into Jar 2.
Th...

The odds against Arjun solving a problem are $\mathbf{5 : 2}$ and the odds in favour of Bhavana solving the same problem are 3:4. What is the probability that the problem is NOT solved by either of them?

Advika chooses one of three scarves every morning: Red, Blue, or Green.


The probability she chooses Red is $20 \%$.

The probability she chooses Blue is twice the probability of choosing Red.

On the remaining days she wears a Green scarf...

A coffee roaster has $\mathbf{1 2}$ rare coffee beans with intensity scores ranked from $\mathbf{1}$ (mildest) to $\mathbf{1 2}$ (strongest).
You choose 7 beans at random and line them up from mildest to strongest:
$$ C_1< C_2< C_3< C_4< C_...

Cards are numbered from 12 to 51 . Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of $\mathbf{6}$ and the other card is a multiple of $\mathbf{8}$.

If $P(A \cup B)=0.85, P(B)=0.50$ and $P(A \cap B)=0.30$. Then $P\left(A \cap B^{\prime}\right)=$

Vishnu has two jars of marbles, Jar A and Jar B.

Jar A contains 3 yellow marbles and 2 green marbles.
Jar B contains 4 yellow marbles and 3 green marbles.

Vishnu flips a fair coin.

If it lands heads, he picks two marbles at random withou...

A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script that has a constant success rate of $\frac{3}{8}$ per attempt.
If Ishaan initiates the first attempt and they persist u...

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

Vasant and Jothi play a game with a coin. Vasant stakes ₹ 1 and throw the coins four times.
If he throws four heads, he gets his stake and ₹3 from Jothi.
If he throws only three heads and they are consecutive, he gets his stake and ₹2 from ...

A person writes four letters and address four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is

In an entrance test, there are multiple choice questions. There are four possible answers to each question of which only one is correct. The probability that a student knows the answer to a question is $90 \%$. If he gets the correct answer...

Let $A$ and $B$ be two events such that one of the two events must occur. Given that the chance of occurrence of $A$ is $\frac{2}{3}$ the chance of occurrence of $B$, then odds in favour of $B$ is

An unbiased die is tossed twice. What is the probability of getting a 4,5 or 6 on the first toss and a $1,2,3$ or 4 on the second toss?

A pot contains 5 red and 2 green balls. A ball is drawn at random from this pot. If a drawn ball is green, then a red ball is added to the pot. If a drawn ball is red, then a green ball is added to the pot, while the original ball drawn is ...

In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his exp...

If A and B are two events such that $P(\bar{A})=0.3, P(B)=0.4, P(A \cap \bar{B})=0.5$, then find the value of $P(B / A \cup \bar{B})$

Two numbers are selected at random from integers 1 to 9 .
If their sum is even, what is the probability that both the numbers are odd?

Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability o...

Three bags contain a number of red and white balls are as follows.
Bag I: 3 red balls
Bag II: 2 red balls and 1 white ball
Bag III: 3 White balls
The probability that bag $i$ will be chosen and a ball is selected from it is $\frac{i}{6}, i=...

A bag contains $(n+1)$ coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is $\frac{7...

In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are $\frac{1}{2}, \fr...

If for two events $A$ and $B, P(A-B)=\frac{1}{5}$ and $P(A)=\frac{3}{5}$ then $P(B / A)=$

The probability that a randomly chosen number from one to twelve is a divisor of twelve is

A and B each have a calculator which can generate a single digit random number from the set \(\{1,2,3,4,5,6,7,8\}\). They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability t...

An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the thi...

A random variable X with probability distribution is given below

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If the events A and B are mutually exclusive events such that \(P(A)=\frac{1}{3}(3 x+1)\) and \(P(B)=\frac{1}{4}(1-x)\) then the possible values of $x$ lies in the interval

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

What is the probability of a randomly chosen 2 digit number being divisible by 3 ?

While shuffling a pack of cards, 3 cards were accidently dropped, then find the probability that the missing cards belong to different suits?

Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black.
The t...

Let \(\mathrm{A}\) and \({B}\) be two events such that \(P(A / B)=\frac{1}{2}\) and \(P(B / A)=\frac{1}{3}\) and \(P(A \cap B)=\frac{1}{6}\) then, which one of the following is not true?

The probability of inviting three friends on 5 consecutive days, exactly one friend a day and no friend is invited on more than two days is

A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is non-negative?

P and Q are considering to apply for a job. The probability that P applies for the job is \(\frac{1}{4}\). The probability that \(\mathrm{P}\) applies for the job given that \(\mathrm{Q}\) applies for the job is \(\frac{1}{2}\), and the pro...

A and B are two independent events. The probability of their simultaneous occurrence is \(\frac{1}{8}\) and the probability that neither of them occurs is \(\frac{3}{8}\). Then their individual probabilities are

There are some baskets. The chances of picking a loaded basket and choosing a red coloured one is 0.2 . For every 100 tries to pick one basket, 60 times a basket is either loaded or red in colour. What is the probability of choosing an empt...

18 Points are indicated on the perimeter of a triangle \(\mathrm{ABC}\) as shown below. If three points are chosen then probability that it will from a triangle is

A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that the number 5 has appeared atleast once?

The probability distribution of a discrete random variable X is given as

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\(\text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)=\)

Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag...

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will be

If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\frac{3}{2} P(A)\) and \(P(C)=\frac{1}{2} P(B)\), then \(P(A \cup C)\) equals to

Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form the vertices of an isosceles triangle, is

If a number $n$ is chosen at random from the set \(\{11,12,13, \ldots \ldots, 30\}\). Then, the probability that \(n\) is neither divisible by 3 nor divisible by 5, is

A five-digits number is formed by using the digits \(1,2,3,4,5\) with no repetition. The probability that the numbers 1 and 5 are always together, is