HW Specic Instructions 1. Provide appropriate probability statements: P(A), P(A|
ID: 3171095 • Letter: H
Question
HW Specic Instructions
1. Provide appropriate probability statements: P(A), P(A|B), etc.
2. Use appropriate notation.
3. ALL probabilities MUST be reported in 4 decimal digits
The question is...
A recent study investigating the potential association between obesity and asthma interviewed a sample of 11,710 adolescents, recruited from secondary schools of 8 educational districts in France. Each participant completed a self-administered standardized questionnaire including DSM IV (Diagnostic and Statistical Manual of Mental Disorders) questions on eating disorders. The results of the study showed that 7% of the students were classied as asthmatics while 10% of them were classied as obese. Finally, 1% of the students were classied as having both traits. A student from the study is randomly selected.
(a) What is the probability that the student will neither be classied as obese nor as asthmatic?
(b) What is the probability that it has asthma if it is known that he/she is not obese?
(c) What is the probability that the student either is obese or it does not have asthma?
(d) Based on this study, is ”having asthma” statistically independent of ”being obese”? Clearly prove your answer.
Explanation / Answer
probabilty of having asthema =P(A)=0.07
probabiltyof being obese =P(B)=0.1
and probability of being both =P(AnB)=0.01
a)here P(AUB)=P(A)+P(B)-P(AnB)=0.07+0.1-0.01=0.16
hence probability that the student will neither be classied as obese nor as asthmatic=1-P(AUB)=1-0.16=0.84
b) P(AnBc)=P(A)-P(AnB)=0.07-0.01=0.06
probability that it has asthma if it is known that he/she is not obese =P(A|Bc)=P(AnBc)/P(Bc)=0.06/0.9=0.0667
c)probability that the student either is obese or it does not have asthma =P(BUAc)=1-(P(A)-P(AnB))=1-(0.07-0.01)
=0.94
d)as P(AnB) is not equal to P(A)*P(B) they are not statistically independent
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