conditional probability

A box contains the following three coins. I. A fair coin head on one face and tail on the other face. II. A coin with heads to both the faces. III. A coin with tails on both the fa...

$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2 X-6$, the conditional probability $P(Y \leq 7 \mid X \geq 5)$ (rounded off to...

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by $F_Z(x) = \begin{cases} 1 - e^{-x} & \text{if } x \ge 0 \\ 0 & \...

Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a probability $${1 \over 5}$$ of losing an incoming parcel, indepen...

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at rando...

Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4...

An examination consists of two papers, paper $$1$$ and paper $$2.$$ The probability of failing in paper $$1$$ is $$0.3$$ and that in paper $$2$$ is $$0.2.$$ Given that a student ha...