JEE MAIN Probability Conditional Bays Previous Year Questions (PYQs)

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 :

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

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:

$ \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:

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:

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:

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 :

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: