JEE Main 2015 — Probability & Statistics

If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is

Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X)$, with replacement, then the probability that $A$ and $B$ have equal number of elements is:

If the mean and the variance of a binomial variate $X$ are $2&1$ respectively, then the probability that $X$ takes a value greater than or equal to one is:

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is:

A factory is operating in two shifts, day and night, with $70$ and $30$ workers, respectively.If per day mean wage of the day shift workers is, $₹54$ and per day mean wage of all the workers is $₹60$, then per day mean wage of the night shift workers (in $₹$) is :

The mean of a data set comprising of $16$ observations is $16$. If one of the observation value $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data is