Answer:
Probability that a student chosen randomly from the class plays basketball or baseball is
or 0.76
Step-by-step explanation:
Given:
Total number of students in the class = 30
Number of students who plays basket ball = 19
Number of students who plays base ball = 12
Number of students who plays base both the games = 8
To find:
Probability that a student chosen randomly from the class plays basketball or baseball=?
Solution:
---------------(1)
where
P(A) = Probability of choosing a student playing basket ball
P(B) = Probability of choosing a student playing base ball
P(A \cap B) = Probability of choosing a student playing both the games
<u>Finding P(A)</u>
P(A) = ![\frac{\text { Number of students playing basket ball }}{\text{Total number of students}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20Number%20of%20students%20playing%20basket%20ball%20%7D%7D%7B%5Ctext%7BTotal%20number%20of%20students%7D%7D)
P(A) =
--------------------------(2)
<u>Finding P(B)</u>
P(B) = ![\frac{\text { Number of students playing baseball }}{\text{Total number of students}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20Number%20of%20students%20playing%20baseball%20%7D%7D%7B%5Ctext%7BTotal%20number%20of%20students%7D%7D)
P(B) =
---------------------------(3)
<u>Finding
</u>
P(A) = ![\frac{\text { Number of students playing both games }}{\text{Total number of students}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20Number%20of%20students%20playing%20both%20games%20%7D%7D%7B%5Ctext%7BTotal%20number%20of%20students%7D%7D)
P(A) =
-----------------------------(4)
Now substituting (2), (3) , (4) in (1), we get
![P(A \cup B)= \frac{19}{30} + \frac{12}{30} -\frac{8}{30}](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%3D%20%5Cfrac%7B19%7D%7B30%7D%20%2B%20%5Cfrac%7B12%7D%7B30%7D%20-%5Cfrac%7B8%7D%7B30%7D%20)
![P(A \cup B)= \frac{31}{30} -\frac{8}{30}](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%3D%20%5Cfrac%7B31%7D%7B30%7D%20-%5Cfrac%7B8%7D%7B30%7D%20)
![P(A \cup B)= \frac{23}{30}](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%29%3D%20%5Cfrac%7B23%7D%7B30%7D)