The probability that a student participates in both sports and music is 108/1376
Explanation:
Let x be the number of students participating in both sports and music
According to the question:
P(A or B) = P(A) + P(B) - P(A and B)
P(sports or music) = P(sports) + P(music) - P(sports and music)
[tex]\frac{974}{1376} = \frac{649}{1376} + \frac{433}{1376} - \frac{x}{1376} \\\\974 = 1082 - x\\\\x = 108[/tex]
P(sports and music) = [tex]\frac{108}{1376}[/tex]
Therefore, the probability that a student participates in both sports and music is 108/1376
