Practice Final, B9
I got (49/282) x (8 choose 3) x [1- (2/3)^3] The first term represents the P(Alice is infected | she tests positive). The second term decides which 3 of the 8 people she kisses gets infected. The third term represents the P(she infects 3 | she's infected).
rahulchandrupatla: March 18, 2015, 3:24 p.m.
Is the conditional probability in the third term redundant as you already found the probability she's infected in the first term?
PeterH: March 18, 2015, 3:53 p.m.
I got something different for the first term. I think it's $\frac{(.98)(.1)}{(.98)(.1)+(.1)(.9)}$ which is $\frac{49}{94}$
Viridiana: March 18, 2015, 6:16 p.m.
I'm kind of confused on this one. It tells us that she tested positive, not that she has the disease. So do we consider the possibility that she does not have the disease? or do we just proceed by first calculating that she has the disease given that she test positive?
jferrermartinez: March 18, 2015, 11:20 p.m.
Oh yeah, Peter H, you're right. P(Alice has the disease | she tests +) = 49/94. I don't know why, but for the first term in my original post (49/282), I got that by multiplying the probability (Alice has the disease given she tested positive) by the 1/3 probability of contracting the disease through kissing. This is equal to the P(Alice infects one person with one kiss). I don't really know if we need this term anywhere, though.
Alan_Mendoza: March 19, 2015, 6:01 p.m.
Viridiana, we do not consider the possibility that she does not have the disease because the question asks us what the probability is of her passing on the disease to 3 people, for that she must have the disease.
Alan_Mendoza: March 19, 2015, 6:08 p.m.
Can't we multiply the first term by (8choose3 x (1/3)^3 x (1-(1/3))^5) ?
aHean: March 19, 2015, 7:06 p.m.
Alan, I believe you are correct. That accounts the 1/3 chance of being infected occurring 3 times as well as her NOT infecting the other 5 people.
Soniakumr: March 19, 2015, 7:54 p.m.
Alan, I got that same answer, the first term times (8choose3 x (1/3)^3 x (1-(1/3))^5).
Lilyhui: March 19, 2015, 9:11 p.m.
Same answer!