

Subject:
Probability Question
Category: Science > Math Asked by: roadapplesga List Price: $4.50 
Posted:
09 Feb 2003 15:19 PST
Expires: 11 Mar 2003 15:19 PST Question ID: 159203 
Males and females are observed to react differently to a given set of circumstances. It has been observed that 70% of the females react positively to these circumstances, whereas only 40% of males react positively. A group of 20 people, 15 female and 5 male, was subjected to these circumstances, and the subjects were asked to describe their reactions on a written questionnaire. A response picked at random from the 20 was negative. What is the probability that it was of a male? Thanks in advance! 

Subject:
Re: Probability Question
Answered By: hailstormga on 09 Feb 2003 17:06 PST Rated: 
roadapples, Following the trail of information we are given, we see that out of 15 women, 70% of them should give a positive response. This would give us 10.5 women with a positive result, and 4.5 women with a negative result (I'll ignore the question of what 0.5 women is supposed to be, since it is ultimately not relevant to the final answer) Meanwhile, out of 5 men, 40% would have a positive reaction, meaning that 2 men would give a positive reaction, while 3 would give a negative one. This means we have 7.5 total negative reactions, 3 of which come from males. Dividing 3 by 7.5 gives us the result that 40% of all of the negative responses in this study should come from males. So the probability that a randomly selected negative response from a pool of 15 females and 5 men is from a male is 40%. 
roadapplesga
rated this answer:
and gave an additional tip of:
$1.25
Thanks for the answer! 

Subject:
Re: Probability Question
From: mathtalkga on 09 Feb 2003 18:37 PST 
I agree with hailstormga's answer. The mathematical name for this sort of argument is Bayesian inference. There is a specific formula (Bayes formula) that expresses the conditional probability. To apply Bayes formula (as hailstromga did above in words), let: M = response from male F = response from female (complementary event to above) N = response is negative Then the application of Bayes formula: P( M  N ) = P( N  M ) * P( M )  P( N  M )*P( M ) + P( N  F )*P( F ) where the denominator represents an expansion of P( N ). Plugging in the various data given in the problem, Bayes formula evaluates to: (.60)*(.25)  (.60)*(.25) + (.30)*(.75) = (.15)/(.375) = 40% Bayes formula can be derived easily from the definition of conditional probability. regards, mathtalkga 
Subject:
Re: Probability Question
From: ivlesga on 09 Feb 2003 19:46 PST 
Wow, mathtalkga, you surely likes math! Me too, although, I'm not very good at math anymore :( I'm going to sue my teachers in high school, I wish you're my teacher, LOL! 
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