Intro Statistics combination/probability problems.

[nontradstuden]

Hello. Am I counting right with these problems? I can't remember exactly how they were worded, but I remember what they were asking...

1) Given 20 men and 20 women, how many groups of 12 can you make with 6 men and 6 women.

I said 20.Combination.6 * 20.Combination.6.

2) given S= {1, 2, 4, 5, 7}, you will choose 3 randomly from the set. What's the probability of getting an even number greater than 500?

I said 12 / 5.Permutation.3.

How I got 12:

1. 3 ways of having 5 first, 2 last.
2. 3 ways of having 5 first, 4 last.
3. 3 ways of having 7 first, 2 last.
4. 3 ways of having 7 first, 4 last.

Added it up to get 12. I then divided it by a permutation because order is important?...


3) What is the probability that two randomly chosen people were both not born in June?

I said P(First not born in June ^ Second not born in June)= (11/12) * (11/12)



Is my counting right? Thanks for your help.

 

[Ray Vickson]

Hello. Am I counting right with these problems? I can't remember exactly how they were worded, but I remember what they were asking...

1) Given 20 men and 20 women, how many groups of 12 can you make with 6 men and 6 women.

I said 20.Combination.6 * 20.Combination.6.

2) given S= {1, 2, 4, 5, 7}, you will choose 3 randomly from the set. What's the probability of getting an even number greater than 500?

I said 12 / 5.Permutation.3.

How I got 12:

1. 3 ways of having 5 first, 2 last.
2. 3 ways of having 5 first, 4 last.
3. 3 ways of having 7 first, 2 last.
4. 3 ways of having 7 first, 4 last.

Added it up to get 12. I then divided it by a permutation because order is important?...


3) What is the probability that two randomly chosen people were both not born in June?

I said P(First not born in June ^ Second not born in June)= (11/12) * (11/12)



Is my counting right? Thanks for your help.

You counting for (2) is incorrect. If you first pick 5, then picking any two other numbers gives you a result > 500. If you first pick 7, then picking any two other numbers gives you a result > 500. If you pick anything other than 5 or 7 first you will not get a result > 500.

RGV

 

[nontradstuden]

@Ray Vickson,

Thanks for your help.

For number 2, they have to be even and >500, how do I go about solving that part?

 

[Ray Vickson]

@Ray Vickson,

Thanks for your help.

For number 2, they have to be even and >500, how do I go about solving that part?

Surely you know what an even number looks like!

RGV