Problem #4:
In addition to a small amount of number crunching, this problem also asks you to make sure you can keep track of identifiers such as ‘X’, ‘N’, or ‘P’ as specified in the problem. In other words, you must make sure that you are clear about what each of these variables represents.
At a certain HIV clinic, 29% of the people who come in for testing are found to be HIV positive. (As with problem #1, this is a made-up number – real life findings are, I’m happy to report, not this high!)
Suppose that you choose three patients at random so that each has probability 0.29 of being HIV positive, and that they are independent of each other. Let the ‘X’ represent the number of HIV-positive individuals in your sample of three people.
P(HIV+) = .29 P(HIV-) = .71
a) What are the possible values of X?
S = {0,1,2,3}
b) Consider these three individuals. There are 8 possible arrangements of HIV positive and HIV negative. For example, we might use the symbol NNP to indicate that first two are HIV negative, and the third is HIV positive. What are the 8 possible arrangements? What is the probability of each of these 8 arrangements?
P(X=0) = P(NNN) = 1/8
P(X=1) = P(NNP or NPN or PNN) = P(NNP) + P(NPN) + P(PNN) = 3/8
P(X=2) = P(NPP or PNP or PPN) = P(NPP) + P(PNP) + P(PPN) = 3/8
P(X=3) = P(PPP) = 1/8
c) Think about what we mean when we say ‘X’. Then provide the value of X for each arrangement in question ‘b’. Then calculate the probability of each possible value of X.
d) Why was it important that I specify in the question that “they are independent of each other”?
I have an issue understanding how to incorporate the .29 into this problem, is it part C?
In addition to a small amount of number crunching, this problem also asks you to make sure you can keep track of identifiers such as ‘X’, ‘N’, or ‘P’ as specified in the problem. In other words, you must make sure that you are clear about what each of these variables represents.
At a certain HIV clinic, 29% of the people who come in for testing are found to be HIV positive. (As with problem #1, this is a made-up number – real life findings are, I’m happy to report, not this high!)
Suppose that you choose three patients at random so that each has probability 0.29 of being HIV positive, and that they are independent of each other. Let the ‘X’ represent the number of HIV-positive individuals in your sample of three people.
P(HIV+) = .29 P(HIV-) = .71
a) What are the possible values of X?
S = {0,1,2,3}
b) Consider these three individuals. There are 8 possible arrangements of HIV positive and HIV negative. For example, we might use the symbol NNP to indicate that first two are HIV negative, and the third is HIV positive. What are the 8 possible arrangements? What is the probability of each of these 8 arrangements?
P(X=0) = P(NNN) = 1/8
P(X=1) = P(NNP or NPN or PNN) = P(NNP) + P(NPN) + P(PNN) = 3/8
P(X=2) = P(NPP or PNP or PPN) = P(NPP) + P(PNP) + P(PPN) = 3/8
P(X=3) = P(PPP) = 1/8
c) Think about what we mean when we say ‘X’. Then provide the value of X for each arrangement in question ‘b’. Then calculate the probability of each possible value of X.
d) Why was it important that I specify in the question that “they are independent of each other”?
I have an issue understanding how to incorporate the .29 into this problem, is it part C?