Basic Probability

[rebecca515]

I never can get these problems right so would someone mind solving it step by step for me, so i can understand it better?

 

[Dr.Peterson]

This is a very tricky table; it could be explained a lot better, but you can figure out what it means by paying close attention.

I suggest that you first consider these questions and tell us your answers; once the meaning is clear, you can consider answering the question. But since the question is about men, we can ignore the women for now.

1. Looking at the first column under Men, what does each number mean? (Think about the sum of the column, as well as its label.)
2. What does each number in the second column under Men mean?
3. Suppose the population consists of 1000 men. How many are in each age group?
4. How many in each age group are never married?
5. How many in each age group have been married?

 

[Steven G]

1) Notice that men and women are not considered together on this chart. The rows for women all add to 100% The rows for men all add to 100%. The columns all add to 100%. It is important to observe the structure so we can have a clue what kind of information exists. In particular, we CANNOT answer, "What is the proportion of men in the population?" Unless we know the relative sizes of the male population and female population, we can't answer that question.

2) Likewise, we cannot tell the proportion of unmarried men vs. married men for the entire population (or women). Again, without the relative sizes of the population in the two groups, the question remains a mystery.

3) Read the question VERY CAREFULLY. It asks only about a single column from the table. Which one?

4) Answer the question.

Unless I am missing something, no column nor row adds up to 1.

 

[Dr.Peterson]

Unless I am missing something, no column nor row adds up to 1.

The Proportion in Population columns add to 1 close enough for statistical work.

The others don't; that's why I asked my interpretation questions, which require a closer look at meanings, in part based on what doesn't add to 1.

 

[Dr.Peterson]

Right. I get a little carried away. There are sums to unity in horizontal pairs only.

I don't see any such pairs, either -- until I added a couple columns and made it that way, as part of solving the problem.

@rebecca515, can you respond with a little work so we can discuss this more specifically?

 

[tkhunny]

Wow. Super not paying attention. Off to spend sometime in the corner.

Seriously, if I had been compelled to testify in court, I would have said those two columns were "Never Married" and "Ever Married", making them mutually exclusive and summing to unity. It just doesn't say that. :-(