Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

This question assesses the students understanding of what it means for two events to be independent or dependent. Specifically, if two events are independent then the outcomes of one event do not affect the outcomes of the other event.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Basic probability skills involving coins, dice and other events with equally likely outcomes.

Basic data structures and maths/stats functionality given.

You can configure the rest.

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When throwing a dice once what is the probability of ....

rebelmaths

r digits are picked at random (with replacement) from the set $\{0,\;1,\;2,\ldots,\;n\}$. Probabilities that 1) all $\lt k$, 2) largest is $k$?

A box contains $m$ white balls and $n$ black balls. A ball is drawn out of the box at random. What is the probability that the ball is black/white?

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

Two numbers from a set of $5$ numbers are chosen at random, without replacement. Find the distribution $X$ of their sum and $E[X]$.

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

The random variable $X$ has a PDF which involves a parameter $k$. Find the value of $k$. Find the distribution function $F_X(x)$ and $P(X \lt a)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.