Intro Statistics combination/probability problems.

In summary: Ray Vickson,In summary, The conversation discusses counting and probability problems involving combinations, permutations, and the probability of two randomly chosen people not being born in June. The correct solution for the second problem is given as picking 5 or 7 first and then any two other numbers to get a result greater than 500. The conversation also acknowledges that an even number is necessary for the second problem.
  • #1
nontradstuden
54
0
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.
 
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  • #2
nontradstuden said:
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
 
  • #3
@Ray Vickson,

Thanks for your help.

For number 2, they have to be even and >500, how do I go about solving that part?
 
  • #4
nontradstuden said:
@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
 

Related to Intro Statistics combination/probability problems.

1. What is the difference between combination and probability problems in Intro Statistics?

Combination problems involve counting the number of ways to choose a subset of items from a larger group, while probability problems involve calculating the likelihood of a certain event occurring based on a given set of data.

2. How do you calculate the number of combinations in a given situation?

The formula for calculating the number of combinations is nCr = n! / (r! * (n-r)!), where n represents the total number of items and r represents the number of items being chosen.

3. What is the difference between permutations and combinations?

Permutations involve arranging items in a certain order, while combinations do not take into account the order of the items.

4. How do you use probability to solve real-world problems?

To use probability to solve real-world problems, you must first identify the event or outcome you are interested in and then gather data to calculate the probability of that event occurring. You can then use this probability to make informed decisions or predictions.

5. Can probability be used to predict the future?

No, probability cannot be used to predict the future with certainty. It can only provide a likelihood or chance of a certain event occurring based on past data and assumptions. Other factors, such as chance and human behavior, can also influence the outcome of events.

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