Answer:
Probability that a student chosen randomly from the class plays basketball or baseball is [tex]\frac{23}{30}[/tex] 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:
[tex]P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]---------------(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
Finding P(A)
P(A) = [tex]\frac{\text { Number of students playing basket ball }}{\text{Total number of students}}[/tex]
P(A) = [tex]\frac{19}{30}[/tex]--------------------------(2)
Finding P(B)
P(B) = [tex]\frac{\text { Number of students playing baseball }}{\text{Total number of students}}[/tex]
P(B) = [tex]\frac{12}{30}[/tex]---------------------------(3)
Finding [tex]P(A \cap B)[/tex]
P(A) = [tex]\frac{\text { Number of students playing both games }}{\text{Total number of students}}[/tex]
P(A) = [tex]\frac{8}{30}[/tex]-----------------------------(4)
Now substituting (2), (3) , (4) in (1), we get
[tex]P(A \cup B)= \frac{19}{30} + \frac{12}{30} -\frac{8}{30} [/tex]
[tex]P(A \cup B)= \frac{31}{30} -\frac{8}{30} [/tex]
[tex]P(A \cup B)= \frac{23}{30}[/tex]
