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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Probability Conditional Bays PYQ

JEE MAIN PYQ
In a bolt factory, machines $A, B$ and $C$ manufacture respectively $20 \%, 30 \%$ and $50 \%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine $C$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
$ \text{The area of the region } {(x,y): x^{2}\le y \le 8-x^{2},; y\le 7} \text{ is:} $





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
A company has two plants $A$ and $B$ to manufacture motorcycles. $60%$ are made at $A$ and $40%$ at $B$. Of these, $80%$ of $A$’s and $90%$ of $B$’s motorcycles are of standard quality. A randomly picked motorcycle from the total production is found to be of standard quality. If $p$ is the probability that it was manufactured at plant $B$, then $126p$ equals:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $

$ \begin{array}{lccc} & \text { Red } & \text { Blue } & \text { Green } \\ \text { Bag I } & 3 & 2 & 5 \\ \text { Bag II } & 4 & 3 & 3 \\ \text { Bag III } & 5 & 1 & 4 \end{array} $

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
A bag contains 8 balls, whose colours are either white or black. Four balls are drawn at random without replacement and it is found that 2 balls are white and the other 2 balls are black. The probability that the bag contains an equal number of white and black balls is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

JEE MAIN PYQ
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\dfrac{m}{n}$, where $\gcd(m,n)=1$, then $m+n$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12 x^2-7 x+1=0$, then the value of $\frac{P(\bar{A} \cup \bar{B})}{P(\bar{A} \cap \bar{B})}$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
Three urns $A$, $B$ and $C$ contain $(7\text{ red}, 5\text{ black})$, $(5\text{ red}, 7\text{ black})$ and $(6\text{ red}, 6\text{ black})$ balls, respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn $A$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Solution


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