Respuesta :
Answer:
The probability of getting someone who tests positive, given that he or she had the disease is 0.8954.
Step-by-step explanation:
The data provided is:
YES NO Total
Positive 137 8 145
Negative 16 139 155
Total 153 147 300
An individual is selected at random from the group.
We need to compute the probability of getting someone who tests positive, given that he or she had the disease.
The conditional probability of an event A given that another event B has already occurred is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)}[/tex]
Let A = individuals who tests positive and B = individual who had the disease.
The number of individuals who tests positive and had the disease is,
n (A ∩ B) = 137
n (B) = 153
Compute the conditional probability of A given B as follows:
[tex]P(A|B)=\frac{n(A\cap B)}{n(B)}[/tex]
[tex]=\frac{137}{153}[/tex]
[tex]=0.8954[/tex]
Thus, the probability of getting someone who tests positive, given that he or she had the disease is 0.8954.
