Amit M Agarwal Solutions for Chapter: Advanced Probability, Exercise 3: Work Book Exercise 16.3

Suppose $X$ has a Binomial distribution $B\left(6,\frac{1}{2}\right)$. Then which of the outcome is most likely?

A discrete random variable $X$ has the following probability distribution

The value of $C$ and the mean of the distribution are

The probability of guessing correctly atleast $8$ out of $10$ answers on a true-false examination is

Ravish and Vineet decided to meet on New Year's day evening at a place in Cannaughi Place between $7\mathrm{pm}$ and $8\mathrm{pm}$. The first one to arrive waits for $15 \min$ and then leave. Assuming that each is independently equally likely to arrive at any time during the hour (between $7\mathrm{pm}$ and $8\mathrm{pm}$), then the probability that they meet is

If a rod of length $a$ is broken into three parts at random, then the probability that a triangle can be formed from these parts, is

If two numbers $x$ and $y$ are chosen such that $x\in \left[0,4\right]$ and $y\in \left[0,4\right]$, then the probability that the chosen number satisfy the inequation $y^2\le x,$ is

With the vertices of a square as centres, four ellipses are drawn to pass through the centre and the middle points of its sides, the probability that a point of the square chosen at random will lie within any two of the ellipses, is

The outcomes of an experiment are represented by points in the square bounded by $x=0, y=0, x=2$ and $y=2$ in $XY$-plane. If the probability is distributed uniformly, then the probability that $x^2+y^2>1$ is