'Simple' Prob. question that has confused me: Shawn, Andrea, & spinner game

[Simonsky]

The question is no. 6 on this page: ( hope you can read it-have had trouble getting files accepted so use low resolution, maybe too low!)




I might be misinterpreting the wording of the question which seems somewhat 'polysemic' to me!

The circle is divided into 12 segments with 5 Pink 4 Blue and 3 green.

As it is the first go of the game there is no score as yet so I wasn't sure whether , on a first go, the green numbers are doubled. If they are, then all the greens will produce a score higher than three with a theoretical probability of 3/12 (1/4). If the scores aren't doubled on the first go ( or halved in the case of blue) then then it is still 1/4.

Yet the answer is 1/6 which I don't get as each go will have the same probabilities.

I know I'm missing something obvious that will cause me to go 'D'oh!', slap my forehead and think of myself as a no-hoper extraordinaire-so sock it to me!

 

[Dr.Peterson]

The question is no. 6 on this page: ( hope you can read it-have had trouble getting files accepted so use low resolution, maybe too low!)

I might be misinterpreting the wording of the question which seems somewhat 'polysemic' to me!

The circle is divided into 12 segments with 5 Pink 4 Blue and 3 green.

As it is the first go of the game there is no score as yet so I wasn't sure whether , on a first go, the green numbers are doubled. If they are, then all the greens will produce a score higher than three with a theoretical probability of 3/12 (1/4). If the scores aren't doubled on the first go ( or halved in the case of blue) then then it is still 1/4.

Yet the answer is 1/6 which I don't get as each go will have the same probabilities.

I know I'm missing something obvious that will cause me to go 'D'oh!', slap my forehead and think of myself as a no-hoper extraordinaire-so sock it to me!

As to the file, its resolution is fine. One trick that was recently mentioned was to display a picture on your screen, and use Windows' Snipping Tool or something similar to get an image that has just about the right resolution. I did that, and here's my result (a little smaller file than your whole page):


As for being polysemic, I'd just call the question ambiguous, or poorly written. (But that's a nice word.) In my mind, nothing is ever said about how many turns they take, and doubling or halving the score that is printed right there is so odd my mind wants to find other meanings.

But I see the same answer you do for the problem; though I've come back to this question a couple times, no other interpretation I can think of makes sense, and none gives 1/6 as an answer. Are you sure you looked at the right one? But answers in books are wrong more often than you would like to accept.

And even if it turns out that we both missed something, you've done some very good thinking, so don't let it get to you.

 

[Simonsky]

(As for being polysemic, I'd just call the question ambiguous, or poorly written. (But that's a nice word.) In my mind, nothing is ever said about how many turns they take, and doubling or halving the score that is printed right there is so odd my mind wants to find other meanings.

But I see the same answer you do for the problem; though I've come back to this question a couple times, no other interpretation I can think of makes sense, and none gives 1/6 as an answer. Are you sure you looked at the right one? But answers in books are wrong more often than you would like to accept.

And even if it turns out that we both missed something, you've done some very good thinking, so don't let it get to you.[/QUOTE])

Thanks for your reply which is appreciated as always. Well, you've boosted my confidence somewhat, for which I thank you. As you will know from our previous interchanges, I'm still in the early days of building confidence in mathematical thinking and tend to think I'm going wrong all the time and missing the obvious (because I'm prone to that!). I suspected that it was a poorly worded question but needed but I needed to check it out with someone experienced. it's good that you reminded me that textbooks are fallible, I've come across that before but it's hard to know when you are still on the lowest slopes of mathematics.

Thanks for your words of encouragement which are meaningful and genuinely helpful to me.

 

[JeffM]

You are correct that the problem is very badly posed. As a physical matter, the probability that the spinner will have an equal probability of landing in any sector is absurd. But this is math, and we assume an ideal world, where there is an equal probability that the spinner will land in any of the 12 sectors. Given that the first person spins and lands on a pink 3, that person's score is 3. There are five pink sectors, each with a score of 3. There four blue sectors, each with a score that is less than or equal to 3. There are three green sectors, with scores that are greater than or equal to 4. Thus, the probability of beating a score of 3 is

\(\displaystyle \dfrac{3}{12} = \dfrac{1}{4} \ne \dfrac{1}{6}.\)

 

[mmm4444bot]

I think each player gets only one spin. I don't understand why they don't simply print the final score on each sector, instead of displaying it only on the red ones. That is, if the score on a blue sector is 10, why display it as 5 and make the player double it?