conditional probability

Consider discrete random variables X and Y with probabilities as follows: P(X = 0 and Y = 0) = $\frac{1}{4}$ P(X = 1 and Y = 0) = $\frac{1}{8}$ P(X = 0 and Y = 1) = $\frac{1}{2}$ P...

Consider discrete random variable $X$ and $Y$ with probabilities as follows: $$ \begin{aligned} & P(X=0 \text { and } Y=0)=\frac{1}{4} \\ & P(X=1 \text { and } Y=1)=\frac{1}{8} \\...

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the s...

A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probabili...

A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is