Given:
Nancy decides to roll a dice three times.
To find:
The probability that she will roll all even numbers.
Solution:
If a dice is rolled, then the possible numbers are
Total number = {1,2,3,4,5,6} = 6
Even numbers = {2,4,6} = 3
Odd numbers = {1,3,5} = 3
Probability of getting an even number [tex]=\dfrac{\text{Even number}}{\text{Total numbers}}[/tex]
[tex]P(\text{Even})=\dfrac{3}{6}[/tex]
[tex]P(\text{Even})=\dfrac{1}{2}[/tex]
So, probability of getting all even numbers is
[tex]P(\text{All even})=P(\text{Even})\times P(\text{Even})\times P(\text{Even})[/tex]
[tex]P(\text{All even})=\dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2}[/tex]
[tex]P(\text{All even})=\dfrac{1}{8}[/tex]
Therefore, the required probability is [tex]P(\text{All even})=\dfrac{1}{8}[/tex].
The probability that Nancy will roll all even numbers will be:
"[tex]\frac{1}{8}[/tex]".
According to the question,
Number of times dice rolled = 3
Total numbers = {1, 2, 3, 4, 5, 6}
= 3
Even numbers = {2, 4, 6}
= 3
Odd numbers = {1, 3, 5}
= 3
Now,
The probability of getting even numbers will be:
= [tex]\frac{Even \ numbers}{Total \ numbers}[/tex]
= [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex]
hence,
The required probability be:
= P(Even) × P(Even) × P(Even)
= [tex]\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}[/tex]
= [tex]\frac{1}{8}[/tex]
Thus the above answer is correct.
Find out more information about probability here:
https://brainly.com/question/24756209
