Probability of a Group Taking a Class

[dreamingotter]

A group of athletes (There are 50 athletes) is split into 10 different groups randomly. And 5 athletes randomly take a class, independent of the group they are assigned to.
What is the probability that group 1 has no athlete that's taking the class?
Also, what is the probability that both groups 1 and 2 have no athletes taking the class?

 

[Dr.Peterson]

What help do you need with this? Please show us what you have tried and where you are stuck. (See our submission guidelines.) We need to know what methods you are learning in order to provide the right help.

Also, are the groups all the same size? I'm guessing that each has 5 members, but we need to be sure.

 

[dreamingotter]

Yes, the groups are all the same size, so each group has 50 members. I am learning about the summation of expectations, which is why I want to calculate the probability that group 1 has no athlete in the class.

 

[dreamingotter]

Ooh, I think I got it. Can somebody confirm?

The first one would be: (45 choose 5)/(50 choose 5) because you have 50C5 way of selecting the athletes in the group and out of the 45 who are not taking the class, you select 5.

 

[Steven G]

[

Ooh, I think I got it. Can somebody confirm?

The first one would be: (45 choose 5)/(50 choose 5) because you have 50C5 way of selecting the athletes in the group and out of the 45 who are not taking the class, you select 5.

Looks good to me. Think hypergeometric for the 2nd one (and even this one!)

 

[Dr.Peterson]

Ooh, I think I got it. Can somebody confirm?

The first one would be: (45 choose 5)/(50 choose 5) because you have 50C5 way of selecting the athletes in the group and out of the 45 who are not taking the class, you select 5.

Correct. And do the same thing for the second part.