# Conditional Probability / Baye's Thm

• Jul 23rd 2011, 07:56 PM
Bushy
Conditional Probability / Baye's Thm
My text is lacking a clear example on this one.

Given the following information

Code:

Prevalence of Alzheimer’s disease (cases per 100)
Age  Group        Males    Females
65-69            1.6      0
70-74              0          2.2
75-79              4.9      2.3
80-84              8.6      7.8
85+                35        27.9

Suppose an unrelated 77 year old man, a 76 year old woman and an 82 year old woman are selected from a community.

1) What is the probability that all three have Alzheimer’s disease?

Let A = 77 year old man has Alzheimer’s
Let B = 76 year old woman has Alzheimer’s
Let C = 82 year old woman has Alzheimer’s

I say the answer is P(A) x P(B) x P(C) = 4.9/100 x 2.3/100 x 7.8/100

2) What is the probability that at least one of the women have Alzheimer’s disease?

Do I need to apply Baye's thm here? Or is it some binomial thing where I find p = 2.3/100 x 7.8/100

3) What is the probability that at least one of the three have Alzheimer’s disease?

If my method for Q2 is correct I would try something similar here.

• Jul 23rd 2011, 10:43 PM
CaptainBlack
Re: Conditional Probability / Baye's Thm
Quote:

Originally Posted by Bushy
My text is lacking a clear example on this one.

Given the following information

Code:

Prevalence of Alzheimer’s disease (cases per 100)
Age  Group        Males    Females
65-69            1.6      0
70-74              0          2.2
75-79              4.9      2.3
80-84              8.6      7.8
85+                35        27.9

Suppose an unrelated 77 year old man, a 76 year old woman and an 82 year old woman are selected from a community.

1) What is the probability that all three have Alzheimer’s disease?

Let A = 77 year old man has Alzheimer’s
Let B = 76 year old woman has Alzheimer’s
Let C = 82 year old woman has Alzheimer’s

I say the answer is P(A) x P(B) x P(C) = 4.9/100 x 2.3/100 x 7.8/100

2) What is the probability that at least one of the women have Alzheimer’s disease?

Do I need to apply Baye's thm here? Or is it some binomial thing where I find p = 2.3/100 x 7.8/100

3) What is the probability that at least one of the three have Alzheimer’s disease?

If my method for Q2 is correct I would try something similar here.