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Phrases Previous Year Questions (PYQs)

Phrases Probability PYQ

Given to events A and B such that odd in favour A are 2 : 1 and odd in favour of $A \cup B$ are 3 : 1. Consistent with this information the smallest and largest value for the probability of event B are given by

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Qus : 2Phrases PYQ

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random then find the probability that no black ball is chosen

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Qus : 3Phrases PYQ

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred is red, is:

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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Qus : 4Phrases PYQ

A computer producing factory has only two plants T₁ and T₂ produces 20% and plant T₂ produces 80% of the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T₁ 10P(computer turns out to be defective given that it is produced in plant T₂ ). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T₂ is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 5Phrases PYQ

Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following statements is true?

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 6Phrases PYQ

If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket?

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 7Phrases PYQ

A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps, he is one step away from the starting point is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 8Phrases PYQ

Two numbers $a$ and $b$ are chosen are random from a set of the first 30 natural numbers, then the probability that $a^2 - b^2$ is divisible by 3 is

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Phrases Previous Year PYQPhrases NIMCET 2019 PYQ

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Qus : 9Phrases PYQ

A committee of 5 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

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 10Phrases PYQ

A critical orthopedic surgery is performed on 3 patients. The probability of recovering a patient is 0.6. Then the probability that after surgery, exactly two of them will recover is

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 11Phrases PYQ

If $0{\lt}P(A){\lt}1$ and $0{\lt}P(B){\lt}1$ and $P(A\cap B)=P(A)P(B)$, then

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 12Phrases PYQ

A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 13Phrases PYQ

A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that is divisible by 3 is

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 14Phrases PYQ

Let A and B be two events defined on a sample space $\Omega$. Suppose $A^C$ denotes the complement of A relative to the sample space $\Omega$. Then the probability $P\Bigg{(}(A\cap{B}^C)\cup({A}^C\cap B)\Bigg{)}$ equals

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 15Phrases PYQ

A coin is thrown 8 number of times. What is the probability of getting a head in an odd number of throw?

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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Qus : 16Phrases PYQ

There are two circles in xy −plane whose equations are $x^2+y^2-2y=0$ and $x^2+y^2-2y-3=0$. A point $(x,y)$ is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

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Qus : 17Phrases PYQ

Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer than 20 minutes for the other. What is the probability that they meet?

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 18Phrases PYQ

Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that

is divisible by 3 is,

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 19Phrases PYQ

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

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

The total number of ways in which numbers can be choosed =25 x 25=625 The number of ways in which either players can choose same numbers = 25

Probability that they win a prize = 25/625 = 1/25

Thus, the probability that they will not win a prize in a single trial = 1 - 1/25 = 24/25

Qus : 20Phrases PYQ

A and B are independent witness in a case. The chance that A speaks truth is x and B speaks truth is y. If A and B agree on certain statement, the probability that the statement is true is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

P(A speaks truth) = x

P(B speaks truth) = y

Since, both A and B agree on certain statement.

Hence, Total Probability =P(A)P(B)+P(A')P(B')

=xy + (1-x)(1-y)

If statement is true then it means both A and B speaks truth.

∴ Required Probability =

Qus : 21Phrases PYQ

In an entrance test there are multiple choice questions, with four possible answer to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then the probability that he as guessing is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

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Qus : 22Phrases PYQ

A man is known to speak the truth 2 out of 3 times. He threw a dice cube with 1 to 6 on its faces and reports that it is 1. Then the probability that it is actually 1 is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

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Qus : 23Phrases PYQ

Let A and B be two events such that

and

where

stands for the complement of event A. Then the events A and B are

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

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Qus : 24Phrases PYQ

If E₁ and E₂ are two events associated with a random experiment such that P (E₂) = 0.35, P (E₁ or E₂) = 0.85 and P (E₁ & E₂) = 0.15 then P(E₁) is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

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Qus : 25Phrases PYQ

The probability of occurrence of two events E and F are 0.25 and 0.50, respectively. the probability of their simultaneous occurrence is 0.14. the probability that neither E nor F occur is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 26Phrases PYQ

If A and B are two events and

, the A and B are two events which are

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

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Qus : 27Phrases PYQ

The probability that a man who is x years old will die in a year is p. Then, amongst n persons $A_1,A_2,\ldots A_n$ each x year old now, the probability that ${{A}}_1$ will die in one year and (be the first to die ) is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 28Phrases PYQ

If a number x is selected at random from natural numbers 1,2,…,100, then the probability for $x+\frac{100}{x}{\gt}29$ is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 29Phrases PYQ

If three thrown of three dice, the probability of throwing triplets not more than twice is

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Phrases Previous Year PYQPhrases NIMCET 2021 PYQ

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Qus : 30Phrases PYQ

A problem in Mathematics is given to 3 students A, B, and C. If the probability of A solving the problem is 1/2 and B not solving it is 1/4 . The whole probability of the problem being solved is 63/64 , then what is the probability of solving it by C?

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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Qus : 31Phrases PYQ

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

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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Probability of winning a prize = $\frac{1}{25}$
Thus, probability of not winning = $1-\frac{1}{25}=\frac{24}{25}$

Qus : 32Phrases PYQ

A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces 20% and plant $T_2$ produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant $T_1$) = 10P (computer turns out to be defective given that it is produced in plant $T_2$). where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

Qus : 33Phrases PYQ

A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely incontradict each other while narrating some incident is

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

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