Respuesta :
Answer: The required probability that the random student selected plays both tennis and basketball is 22%.
Step-by-step explanation: Given that in a school, 40% of the students play tennis, 24% of the students play baseball, and 58% of the students playing neither tennis or baseball.
We are to find the probability that a random student picked plays both tennis and basketball.
Let the total number of students in the school be 100. Also, let T and B represents the set of students who play tennis and basketball respectively.
Then, according to the given information, we have
[tex]n(T)=40,~~~n(B)=24.[/tex]
The number of students who play either tennis or basketball will be represented by T ∪ B.
And so, we have
[tex]n(T\cup B)=100-58=42.[/tex]
We know that the number of students who play both tennis and basketball is denoted by T ∩ B.
From set theory, we get
[tex]n(T\cup B)=n(T)+n(B)-n(T\cap B)\\\\\Rightarrow n(T\cap B)=n(T)+n(B)-n(T\cup B)\\\\\Rightarrow n(T\cap B)=40+24-42\\\\\Rightarrow n(T\cap B)=22.[/tex]
Thus, the required probability that the random student selected plays both tennis and basketball is 22%.
