Question about teaching probability

[Danestress]

I am a bit confused.

 

My math lesson (BJU 6th grade math, lesson 138, for those who want to know) has me the following information to teach probability:

 

Say you gave 20 people a scrap of paper and had them write a number between 1 and 10.

 

There is a chart showing how many people picked each number. For example, 4 out of the 20 wrote the number "7." So the book goes on to show that out of 20 possible answers, seven was picked 4 times, so the probability of picking 7 is 4/20 or 1/5 or 20%.

 

Except that's not right, right? The probability of picking any number is probably the same as a any other right? So really it would be more like 10% right? Or maybe studies who that's not true - that people rarely pick 1 or 10 (let's say) and 7 is therefore slightly more likely to be picked. But either way, a survey of 20 people will hardly be accurate.

 

I hate when I am supposed to teach things that just don't seem right to me!

[Carrie12345]

I am a bit confused.

 

My math lesson (BJU 6th grade math, lesson 138, for those who want to know) has me the following information to teach probability:

 

Say you gave 20 people a scrap of paper and had them write a number between 1 and 10.

 

There is a chart showing how many people picked each number. For example, 4 out of the 20 wrote the number "7." So the book goes on to show that out of 20 possible answers, seven was picked 4 times, so the probability of picking 7 is 4/20 or 1/5 or 20%.

 

Except that's not right, right? The probability of picking any number is probably the same as a any other right? So really it would be more like 10% right? Or maybe studies who that's not true - that people rarely pick 1 or 10 (let's say) and 7 is therefore slightly more likely to be picked. But either way, a survey of 20 people will hardly be accurate.

 

I hate when I am supposed to teach things that just don't seem right to me!

 

In the example, you know for a fact that 4 people wrote 7 and 16 people did NOT write 7. The odds are, indeed, 4/20. But throwing in the option of *chosing which number to write does muck things up a whole bunch for me.

For the record, there won't ever be 20 options when the parameters are numbers 1-10. The maximum amount of options would be 10.

 

ETA: Ds is doing probability now and I HATE IT!

[Jacquelyn in NC]

The probability of an individual person picking 7 is one chance in ten, or 10%. Even though 4 people picked 7 in this problem, which is higher than you might expect, if you repeated the experiment often enough the average number of people to pick 7 would approach 1 person in 10.

 

There may be a second (implied) part to this problem, though. If you took the answers of all 20 people and put them in a hat and picked one, the chances of picking a 7 from THAT pool is indeed 4/20, or 20%.

 

HTH.