NIMCET Probability Previous Year Question Paper and Solution with PDF

Solution

Qus : 2NIMCET 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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Solution

Qus : 3NIMCET 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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Solution

Qus : 4NIMCET 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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Solution

Qus : 5NIMCET 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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Solution

Qus : 6NIMCET 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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Solution

Qus : 7NIMCET 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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Solution

Qus : 8NIMCET 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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Solution

Qus : 9NIMCET 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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Solution

Qus : 10NIMCET 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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Solution

Qus : 11NIMCET 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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Solution

Qus : 12NIMCET 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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Solution

Qus : 13NIMCET 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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Solution

Qus : 14NIMCET 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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Solution

Qus : 15NIMCET 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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Solution

Qus : 16NIMCET 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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Solution

Qus : 17NIMCET PYQ

Region R is defined as region in first quadrant satisfying the condition $x^2 + y^2 < 4$. Given that a point P=(r,s) lies in R, what is the probability that r>s?

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Solution

Qus : 18NIMCET PYQ

If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

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Solution

Qus : 19NIMCET 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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Solution

Qus : 20NIMCET 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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Solution

Qus : 21NIMCET 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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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 : 22NIMCET 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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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 : 23NIMCET 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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Solution

Qus : 24NIMCET 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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Solution

Qus : 25NIMCET 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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Solution

Qus : 26NIMCET 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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Solution

Qus : 27NIMCET 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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Solution

Qus : 28NIMCET PYQ

If A and B are two events and

, the A and B are two events which are

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Solution

Qus : 29NIMCET 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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Solution

Qus : 30NIMCET 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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Solution

Qus : 31NIMCET PYQ

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

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Solution

Qus : 32NIMCET 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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Solution

Qus : 33NIMCET 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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NIMCET Previous Year PYQNIMCET 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 : 34NIMCET 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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Solution

Qus : 35NIMCET 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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