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:
![P(2)=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}](https://tex.z-dn.net/?f=P%282%29%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20favorable%20outcomes%7D%7D%7B%5Ctext%7BNumber%20of%20total%20outcomes%7D%7D)
![P(2)=\dfrac{2}{6}](https://tex.z-dn.net/?f=P%282%29%3D%5Cdfrac%7B2%7D%7B6%7D)
![P(2)=\dfrac{1}{3}](https://tex.z-dn.net/?f=P%282%29%3D%5Cdfrac%7B1%7D%7B3%7D)
Now, the expected number of times when 2 to appear is:
![E(x)=114\times P(2)](https://tex.z-dn.net/?f=E%28x%29%3D114%5Ctimes%20P%282%29)
![E(x)=114\times \dfrac{1}{3}](https://tex.z-dn.net/?f=E%28x%29%3D114%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D)
![E(x)=38](https://tex.z-dn.net/?f=E%28x%29%3D38)
Therefore, the expected number of times is 38.