Let’s play a fun game:
The researchers placed two bags full of red and yellow balls in front of the participants.
In the first pocket, 75 percent of the balls are yellow, and 25 percent are red.
Number two, on the other hand, is 75% red and 25% yellow.
You pick a bag at random and take the balls out one by one, without looking into the bag.
Each time you pull out a ball, you report to the researcher his guess: Are you carrying more yellow or red balls in your bag?
This is a study by Ward Edwards of the University of Michigan, and it’s called:
How humans react to new information in the decision-making process.
The purpose of the experiment is not to test mathematical calculation, but to test human intuition of probability.
Let’s say you touch a red ball and you’re asked to guess, did it come from pocket number one or pocket number two?What are the chances?
If you’re smart enough to say, that’s easy, there are more red balls in number two than there are in number one, then it’s more likely that the ball came from number two.
Then you touch a ball again from the same pocket, again red, and you can adjust your guesses based on this information.
And you think, well, there’s a slightly greater chance that this is a number two pocket.
Then you feel for the third ball from the pocket, which is still red.
(For the above experiment, put the ball back in place each time.)
Notice the crucial question here:
How many times do you think it’s more likely to turn into a number two pocket after you touch the red ball three times?
Please make your own assessment. Keep it in mind.
Then, let’s take a look at the results of that year’s study.
Research shows that:
When the subjects pulled the red ball out of their pocket, they were more likely to think that the red ball was in the majority.
If their first three balls were all red, they were three times more likely to think the bag was predominantly red.
Unfortunately, that estimate is too far off.
How many times does it actually have to be?
(The case above, from Discovery of Thought, I didn’t adjust for the ambiguity of the multiple statement.)
This calculation is simple and interesting, and sometimes very confusing.