that response proved wrong ?
I'm writing an article on the thinking of the probability and statistics for a class of educational psychology . In mathematics there is the idea that people can show why something is true by using a method called "proof by contradiction . " But how that applies to a probability problem ?
For example , let's say two people have completely different answers to this problem . How refute the wrong answer ?
" The probability of deployment of the air bag in a car accident is 0.8 and the probability for cracking windshield is 0.2 . What is the probability that one of the events that occur , but not both ? "
Person A says : " P (A union B ) = 0.8 + 0.2 - (0.8) * (0.2) = 0.84 "
Person B says : " P (A intersect B ^ c ) + P ( A intersect B ^ c ) = 0.68 "
From the psychological point of view , I'm interested in why people think differently in probability and statistics. Each has its own logical way of thinking , but sometimes in mathematics , especially in the probability that the logic could be flawed because it is loaded with too many assumptions or incorrect assumptions .
#1JoannaAnswered at 2012-10-22 04:46:27
First, proof by contradiction is a method used to prove true things first assumption to be false and that shows that the hypothesis does not hold.
For the given problem person A would be correct . And person B has added a third category assume C refers to the intersection of A and B , however this is incorrect .
The best way to show the second person is wrong , this problem is to draw Venn diagrams , it is much easier to see problems like this to think about them conceptually .
In particular mathematics , there is usually only one answer , so that alternative responses will be proven incorrect by the fact that they are not the right answer .
#2SuniAnswered at 2012-12-04 05:56:02
bag deploys = 0.8
bag not implement = 0.2
= 0.2 windshield cracks
windshield does not crack = 0.8
0.8 * 0.2 = 0.16 = bag deploys and windshield cracks
0.8 * 0.8 = 0.64 = bag deploys and the windshield does not crack ***
0.2 * 0.2 = 0.04 = bag does not deploy and windshield cracks ***
0.2 * 0.8 = 0.16 = bag not deployed and the windshield does not crack
0.04 0.64 0.68 = probability of one and not the other
the question relates to one of the events that happen , but not both, and neither involved events .
A and B '
A ' and B
the way they are written are very important questions on probability.
for example. This question should be formulated as :
What is the probability that exactly one event.
this leads to the ambiguity of the question.