Probability · Mathematics · COMEDK
MCQ (Single Correct Answer)
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:
$$ C_1< C_2< C_3< C_4< C_5< C_6< C_7 $$
What is the probability that the third bean $\left(C_3\right)$ has an intensity score of exactly 4 ?
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 without replacement from Jar A.
If it lands tails, he picks two marbles at random with replacement from Jar B.
Given that Vishnu picked one yellow and one green marble, what is the probability that they came from Jar B?
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 $P\left(A \cap B^{\prime}\right)=$
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 until the migration is successful, what is the probability that Kavya is the one who initiates the successful sync?
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 $\frac{\mathbf{1}}{\mathbf{3}}$.
After a win: if she defeats a head, the probability of defeating the next head is $\frac{2}{3}$.
After a loss: if she fails to defeat a head, the probability of defeating the next head is $\frac{\mathbf{1}}{\mathbf{4}}$.
What is the probability that Samhita earns the "Tactical medal"?
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?
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.
Then, a student reaches into Jar 2 and picks two candies.
What is the probability that the student picks two Strawberry candies?
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.
Once a scarf is chosen, she decides whether to wear a Hat (H) and Sunglasses (S).
These choices are independent of each other but depend on the scarf colour:
$$ \begin{array}{|l|l|l|} \hline \text { Scarf colour } & \mathbf{P ( H )} & \mathbf{P ( S )} \\ \hline \text { Red } & 0.5 & 0.8 \\ \hline \text { Blue } & 0.4 & 0.5 \\ \hline \text { Green } & 0.1 & 0.5 \\ \hline \end{array} $$
Advika is spotted outdoors wearing both a Hat and Sunglasses.
What is the probability that she is wearing the Red scarf?
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, with Swarna going first.
If they continue the process until a landing is successful, what is the probability that Sarah is the one who initiates the successful landing?
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 $\frac{7}{12}$, then the value of $n$ is :
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 $\frac{i}{6}, i=1,2,3$. If a white ball is selected, what is the probablity that it came from Bag III
While shuffling a pack of cards, 3 cards were accidently dropped, then find the probability that the missing cards belong to different suits?
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?
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?
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 three cards are mixed and a card is picked randomly. If the upper side of the chosen card is coloured red, what is the probability that the other side is coloured black.
What is the probability of a randomly chosen 2 digit number being divisible by 3 ?
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 probability that Q applies for the job given that P applies for the job is $$\frac{1}{3}$$. Then the probability that $$\mathrm{P}$$ does not apply for the job given that $$\mathrm{Q}$$ does not apply for the job is
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 empty basket plus choosing not a red coloured one.
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 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
A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is non-negative?
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 that the two numbers are equal is
The probability that a randomly chosen number from one to twelve is a divisor of twelve is
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
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 third ball drawn is black is
A random variable X with probability distribution is given below
| $$ \mathrm{X}=x_i $$ |
2 | 3 | 4 | 5 |
|---|---|---|---|---|
| $$ \mathrm{P}\left(\mathrm{X}=x_i\right) $$ |
$$ \frac{5}{k} $$ |
$$ \frac{7}{k} $$ |
$$ \frac{9}{k} $$ |
$$ \frac{11}{k} $$ |
The mean of this distribution is
A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a square $$\}$$, $$\mathrm{B}=\{n \in s: n$$ is a prime$$\}$$ and $$\mathrm{C}=\{n \in s: n$$ is a square$$\}$$. Then, correct order of their probabilities 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
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
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 $$A, B$$ 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
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
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?
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 A and put into bag B. Now one ball is drawn at random from bag B. Given that the drawn ball from B is white, the probability that head appeared on the coin is
$$ \text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)= $$
The probability distribution of a discrete random variable X is given as
| $$\mathrm{X}$$ | 1 | 2 | 4 | 2A | 3A | 5A |
|---|---|---|---|---|---|---|
| $$\mathrm{P(X)}$$ | $$\frac{1}{2}$$ | $$\frac{1}{5}$$ | $$\frac{3}{25}$$ | K | $$\frac{1}{25}$$ | $$\frac{1}{25}$$ |
$$ \text { Then the value of } A \text { if } E(X)=2.94 \text { is } $$
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
The probability of choosing randomly a number c from the set {1, 2, 3, ... 9} such that the quadratic equation $$x^2+4x+c=0$$ has real roots, is
Five persons A, B, C, D and E are in queue of a shop. The probability that A and B are always together is
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is
Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is
If A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2P(B) = 3P(C). What is P(B)?
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing, is
The coefficients a, b and c of the quadratic equation, $$ax^2+bx+c=0$$ are obtained by throwing a dice three times. The probability that this equation has equal roots is
Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals
Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is
If A, B and C are mutually exclusive and exhaustive events of a random experiment such that $$P(B) = {3 \over 2}P(A)$$ and $$P(C) = {1 \over 2}P(B)$$, then $$P(A \cup C)$$ equals
A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is $$p,0 < p < 1$$. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is