JEE Main Mathematics — Probability & Statistics previous year questions with solutions.
Events $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are mutually exclusive events such that $\mathrm{P}(\mathrm{A})=\frac{3 \mathrm{x}+1}{3}, \mathrm{P}(\mathrm{B})=\frac{\mathrm{x}-1}{4}$ and $\mathrm{P}(\mathrm{C})=\frac{1-2 \mathrm{x}}{4}$. The set of possible values of $\mathrm{x}$ are in the interval.
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?
$A$ and $B$ are events such that $P(A \cup B)=3 / 4, P(A \cap B)=1 / 4, P(\bar{A})=2 / 3$ then $P(\bar{A} \cap B)$ is
A problem in mathematics is given to three students $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved is
A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is