I need help with a statistics problem in conditional probability & independence?

Question

The article "Integrating Risk Assessment and Life Cycle Assessment: A Case Study of Insulation" estimates that 5.6% of a certain population has asthma, and that an asthmatic has probability 0.027 of suffering an asthma attack on a given day. A person is chosen at random from this population. What is the probability that this person has an asthma attack on that day?

cidyah · Accepted Answer

Let A = person has asthma
B = suffers from an asthma attack

P(A)=.056
P(B/A)=.027

A person is chosen at random from this population. What is the probability that this person has an asthma attack on that day?
P(A & B) = P(A)P(B/A) = (0.056)(0.027) = .001512

Anonymous · Answer

When they chose a person without astma (94.4%of population): chances for asthma attack=0%. No attack in all cases.
When they chose a person with asthma(5.6% of population): 
- He has no attack in 97.3% of the cases.
- He has an attack in 2.7% of the cases.

So: 
If they pick a person at random:
Probability of asthma attack = 0.056*0.027=...

You will notice that the chance of a random person having an asthma attack is much smaller.

I need help with a statistics problem in conditional probability & independence?

2 Answers