(14.1) Random Variables
A fair 6-sided die
Give your answers as fractions.
$P\left(\text{rolling a 3}\right)=$
$P\left(\text{rolling a 7}\right)=$
$P\left(\text{rolling a number greater than 1}\right)=$For example, $P\left(\text{rolling a 3}\right)$ can be written $P\left(X=3\right)$.
Write the following using $X$.
$P\left(\text{rolling a 6}\right)$ can be written .
$P\left(\text{rolling a number greater than 1}\right)$ can be written
$P\left(\text{rolling a number greater than 2 and less than or equal to 5}\right)$ can be written
Find the following probabilities. Give your answers as fractions.
$P\left(X=1\right)=$ .
$P\left(X\lt 3\right)=$
$P\left(3\le X\lt 6\right)=$
Two fair 6-sided dice
For this experiment where we roll two fair 6-sided dice, let $X$ represent the number of sixes rolled.
For example, $P\left(X=2\right)$ means the probability of rolling 2 sixes.
Find the following probabilities. Give your answers as fractions.
$P\left(X=2\right)=$ .
$P\left(X=1\right)=$
$P\left(X=0\right)=$
| $x$ | $0$ | $1$ | $2$ |
|---|---|---|---|
| $P\left(X=x\right)$ |
Notice that we used $x$ as a variable for the possible outcomes and found $P\left(X=x\right)$.
For example, $P\left(Z=12\right)$ means the probability of the sum of the two numbers equaling 12.
Find the following probabilities. Give your answers as fractions.
$P\left(Z=3\right)=$ .
$P\left(Z=7\right)=$
$P\left(Z\ge 9\right)=$
$P\left(3\le Z\lt 12\right)=$
| $z$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ | $11$ | $12$ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| $P\left(Z=z\right)$ |
A table that contains the probabilities for all possible outcomes is called a
Each probability must be between $\le P\left(X=x\right) \le$ .
The sum of all the probabilities is $\sum P\left(X=x\right)=$ .