1) Considering that a six-sided dice has all these possible numbers as outcomes we can write our sample space:
[tex]1,2,3,4,5,6[/tex]2) So let's calculate the Probabilities:
a) Even number.
Note that we have three even numbers
[tex]1,\mathbf{2},3,\mathbf{4},5,\mathbf{6}[/tex]So we can write the Probability of Even numbers as:
[tex]P(\text{even)}=\frac{3}{6}=\frac{1}{2}[/tex]Note that on the denominator, we place the total possible results, and on the numerator the favorable outcomes.
b) A number > 1
Since we've got 5 favorable events (numbers) greater than 1, we can write out:
[tex]P(>1)=\frac{5}{6}[/tex]c) A number < 6
[tex]P(<6)=\frac{5}{6}[/tex]Note that similarly to the previous item we have 5 favorable outcomes (1,2,3,4,5) in a total of 6 possible results.
d) A Prime number:
In a six-sided die we have the following prime numbers:
[tex]\mathbf{2},\mathbf{3},4,\mathbf{5},6[/tex]So we have 3 favorable outcomes:
[tex]P(\text{prime)}=\frac{3}{6}=\frac{1}{2}[/tex]And that is the answer
