JEE Main 2016 — Probability & Statistics

If $A$ and $B$ are any two events such that $P(A)=\frac{2}{5}$ and $P(A\cap B)=\frac{3}{20},$ then the conditional probability, $P(A|({A}^{'}\cup {B}^{'})),$ where ${A}^{'}$ denotes the complement of $A$, is equal to :

If the mean deviation of the numbers $1, 1+d,\ldots , 1+100d$ from their mean is $255$, then a value of $d$ is :

If the standard deviation of the numbers $2,3,a$ and $11$ is $3.5$, then which of the following is true ?

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If ${E}_{1}$ is the event that die $A$ shows up four, ${E}_{2}$ is the event that die $B$ shows up two and ${E}_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?

The mean of $5$ observations is $5$ and their variance is $12.4$. If three of the observations are $1,2&6$; then the value of the remaining two is :