If the answer is 25%, then the chances of getting it right are 50% since half of the choices are 25%.
But perhaps the stupid bubble sheet reader thinks the answer is “A) 25%” but not “D) 25%” because the statistics grad student teaching the class is a moron.
Or you could argue that the correct answer should be 100% because you never guess wrong. 😀
The answer is write next to it 0% , and if it a SAT style test, the 5th box , other box .
hmm better version would be
A 25 %
B 50 %
C 50 %
D 100%
For pure mathematical evil, the answers should read:
A) 25%
B) 50%
C) 0%
D) 25%
Mike
The answer is 33%. Since there are only three choices, (25, 50, 60), the chance a random choice would yield the correct result is 1/3, or 33%.
I’m still partial to the Monty Hall Question.
Three doors.
There is a prize behind one door, and it does not move.
You get to guess a door.
Monty will always open a door that was neither your choice, nor the prize, and demonstrate “Hey, this choice would have sucked.”
You get to chose again.
Based on the statistics, should you chose the same door you already chose? Or the other one?
You can often get even mathematicians to chose incorrectly, at least until they sit and start enumerating cases.
Based on the statistics, should you chose the same door you already chose? Or the other one?
Always choose the other one. Why? Because the chance you picked a good one when you first chose were 1/3. The chance of picking a good one if you switch is 2/3 since one of the original choices is (effectively) removed from the list.
The correct answer is to not answer, because any answer contradicts itself.
I don’t see this as statistical, more like philosophical. The answer is the letter not the percentage after the letter. if they were all 25% and the correct answer was D you would still only have a 25% random chance of getting it right.
That’s the way I’m reading into it. It says to pick “an answer” in the singular so you only get to pick one of the 4. That in itself brings a distinctness that differentiates A) 25% from D) 25%. A) 25% could in fact be right and D) 25% could be wrong. I think 25% is in there twice just to cause confusion and doubt.
I love that one, Al. I don’t know if I have ever successfully explained it to anyone, though. I try to explain that opening the other door didn’t change the odds you got it right in the first place, and they look at me skeptically and give me a look that says, I don’t think so, but I don’t care enough to argue it.
The easy way to explain it:
P of Door #1 = 1/3. P of every other door = (1 – P of Door #1) = 2/3
Before the revelation, the 2/3 is spread across 2 doors, after revelation, it’s spread across 1. That usually gets the point across since the probabilities above did not change.
Easiest way for folks to wrap their heads around Bayesian stats.
Two arguments I’ve used successfully in convincing someone “Switch, dammit!” is the option of interest.
1) Imagine 1000 doors instead. Pick. 998 empty doors are opened. Now would you switch?
2) Completely enumerate the cases. You have three possible initial choices. There are three initial prize placements -> there’s nine cases. Now: Suppose you -always- stood pat. Look at the cases and tell me the percentage of the time that you’ll win (33). And … what about if you always switched? And if you randomly decided about switching?
Yeah, I’ve tried those. The best response I ever got was when I said: Look at it this way. The host is saying, you can keep the one door, or you can have these two. Oh, and BTW, I’m just going to open one of these other two for you.
Another good one: suppose 5% of the population uses an illegal drug. You have a test which is 95% accurate. You give it to a randomly selected employee and it comes up positive. What are the odds he uses the drug?
I will just go ahead and give the answer: 50/50. If you work it through using Bayesian stats, that is the rather surprising answer.
25% since there are 4 possibilities.
If the answer is 25%, then the chances of getting it right are 50% since half of the choices are 25%.
But perhaps the stupid bubble sheet reader thinks the answer is “A) 25%” but not “D) 25%” because the statistics grad student teaching the class is a moron.
Or you could argue that the correct answer should be 100% because you never guess wrong. 😀
The answer is write next to it 0% , and if it a SAT style test, the 5th box , other box .
hmm better version would be
A 25 %
B 50 %
C 50 %
D 100%
For pure mathematical evil, the answers should read:
A) 25%
B) 50%
C) 0%
D) 25%
Mike
The answer is 33%. Since there are only three choices, (25, 50, 60), the chance a random choice would yield the correct result is 1/3, or 33%.
I’m still partial to the Monty Hall Question.
Three doors.
There is a prize behind one door, and it does not move.
You get to guess a door.
Monty will always open a door that was neither your choice, nor the prize, and demonstrate “Hey, this choice would have sucked.”
You get to chose again.
Based on the statistics, should you chose the same door you already chose? Or the other one?
You can often get even mathematicians to chose incorrectly, at least until they sit and start enumerating cases.
Based on the statistics, should you chose the same door you already chose? Or the other one?
Always choose the other one. Why? Because the chance you picked a good one when you first chose were 1/3. The chance of picking a good one if you switch is 2/3 since one of the original choices is (effectively) removed from the list.
The correct answer is to not answer, because any answer contradicts itself.
I don’t see this as statistical, more like philosophical. The answer is the letter not the percentage after the letter. if they were all 25% and the correct answer was D you would still only have a 25% random chance of getting it right.
That’s the way I’m reading into it. It says to pick “an answer” in the singular so you only get to pick one of the 4. That in itself brings a distinctness that differentiates A) 25% from D) 25%. A) 25% could in fact be right and D) 25% could be wrong. I think 25% is in there twice just to cause confusion and doubt.
I love that one, Al. I don’t know if I have ever successfully explained it to anyone, though. I try to explain that opening the other door didn’t change the odds you got it right in the first place, and they look at me skeptically and give me a look that says, I don’t think so, but I don’t care enough to argue it.
The easy way to explain it:
P of Door #1 = 1/3. P of every other door = (1 – P of Door #1) = 2/3
Before the revelation, the 2/3 is spread across 2 doors, after revelation, it’s spread across 1. That usually gets the point across since the probabilities above did not change.
Easiest way for folks to wrap their heads around Bayesian stats.
Two arguments I’ve used successfully in convincing someone “Switch, dammit!” is the option of interest.
1) Imagine 1000 doors instead. Pick. 998 empty doors are opened. Now would you switch?
2) Completely enumerate the cases. You have three possible initial choices. There are three initial prize placements -> there’s nine cases. Now: Suppose you -always- stood pat. Look at the cases and tell me the percentage of the time that you’ll win (33). And … what about if you always switched? And if you randomly decided about switching?
Yeah, I’ve tried those. The best response I ever got was when I said: Look at it this way. The host is saying, you can keep the one door, or you can have these two. Oh, and BTW, I’m just going to open one of these other two for you.
Another good one: suppose 5% of the population uses an illegal drug. You have a test which is 95% accurate. You give it to a randomly selected employee and it comes up positive. What are the odds he uses the drug?
I will just go ahead and give the answer: 50/50. If you work it through using Bayesian stats, that is the rather surprising answer.