Mathematics Probability & Statistics questions from JEE Main 2003.
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.
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
In an experiment with 15 observations on $x$, the following results were available: $\Sigma x^2=2830, \Sigma x=170$ One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected variance is