Question

Consider the die-toss experiment. Define the following events:
A: {Toss an even number}
B: {Toss a number less than or equal to 3}
a) Describe

Answer 1

A die has 6 sides.

Let X be the outcome of a die-toss

$X =\{1,2,3,4,5,6\}$

Solution A: Toss an even number

$X \, is \, even = \{2,4,6\}$

Solution B: Toss a number less than or equal to 3

$X \leq 3 = \{1,2,3\}$

Solution a) Describe

Assuming a fair die

$p(X = x) = \frac{1}{6}$

$p(X \, is\, even) = p(X =2)+ p(X=4)+ p(X=6)$

$= \frac{1}{6}+\frac{1}{6}+\frac{1}{6} = \frac{1}{2}$

$p(X \leq 3)=p(X=1)+ p(X=2)+ p(X=3)$

$=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2}$