probability

Question

In a P.E. class, 10 students can play basketball, 8 can play paddle tennis, 18 can play kickball, and 4 can play ping pong. What is a student's chances of getting to play paddle tennis?

 

 

 

I thought the answer was 1/5 (8/40= 1/5). But the answer is actually 1/10 and I don't understand that reasoning.

 

Thank you!

Answer 1

Toni,

 

 If I were to take a stab as to why it's 1/10 and not 1/5, it's this:

 

 it says in a P.E. class that students CAN, or are able to, play certain sports. Just because they can, doesn't mean that they have to. They have a choice! So, either they can play, or they do not wish to play. There is a 50/50 chance (or, 1/2) that they will decide to play or not. So, Multiplying your 1/5 by 1/2 gives you 1/10.

 

Now, if we knew more about the students (say, they're really excited for gym that day, so there's a 90% chance that any student would decide to play), then we'd have a different outcome. For the example in parenthesis I just mentioned, we would multiply 1/5 by 9/10 to obtain 9/50 for the student's chances of getting to play paddle tennis.\

 

Hope this helps!

 

If any other tutors have any other thoughts or if I made a mistake, please let me know! Thanks!

 

-Sam