Given:
The faces on a number cube are labeled 1,2,2,3,4, and 5.
The number cube is rolled 114 times.
To find:
How many times would you expect the number 2 to appear?
Solution:
We have,
Total outcomes = 1,2,2,3,4, and 5.
Number of total outcomes = 6
Favorable outcomes = 2 and 2
Number of favorable outcomes = 2
The probability of getting 2 is:
[tex]P(2)=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}[/tex]
[tex]P(2)=\dfrac{2}{6}[/tex]
[tex]P(2)=\dfrac{1}{3}[/tex]
Now, the expected number of times when 2 to appear is:
[tex]E(x)=114\times P(2)[/tex]
[tex]E(x)=114\times \dfrac{1}{3}[/tex]
[tex]E(x)=38[/tex]
Therefore, the expected number of times is 38.
