Question

a medical clinic is randomly selecting two staff members to attend a conference the clinic employees include 7 nurses, 3 doctors, and 2 office staff. the nurses want to know the probability that both attendees will be nurses. the tree diagram displays the possible outcomes of randomly selecting two staff members. which probability is represented by label 3 in the tree diagram?
$\frac{5}{12}$
$\frac{5}{11}$
$\frac{6}{11}$
$\frac{7}{12}$

Explanation:

Step1: Calculate total number of staff members

Total staff members = \(7 + 3+2=12\)

Step2: Analyze the first - selection probability (for label 2)

If label 2 is the probability of selecting a nurse first. Probability of selecting a nurse first \(P(\text{first - nurse})=\frac{7}{12}\). After selecting one nurse, the number of remaining staff members is \(n = 12 - 1=11\), and the number of remaining nurses is \(7-1 = 6\)

Step3: Calculate the conditional probability (for label 3)

Label 3 is the probability of selecting a nurse second, given that a nurse was selected first. Using the formula for conditional probability in a non - replacement situation \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, \(P(\text{second - nurse}|\text{first - nurse})=\frac{6}{11}\)

Answer:

\(\frac{6}{11}\)