Question

the probability that a visit to a primary care physicians (pcp) office results in neither lab work nor referral to a specialist is 28%. of those coming to a pcps office, 26% are referred to specialists and 49% require lab work. determine the probability that a visit to a pcps office results in both lab work and referral to a specialist. what is the probability that a visit results in both lab work and referral to a specialist? choose the correct answer below. a. 0.03 b. 0.18 c. 0.25 d. 0.12 e. 0.49

Explanation:

Step1: Define probabilities

Let $A$ be the event of referral to a specialist, $P(A)=0.26$. Let $B$ be the event of lab - work, $P(B)=0.49$. The probability of neither event $A$ nor event $B$ is $P(\overline{A\cup B}) = 0.28$. Then $P(A\cup B)=1 - P(\overline{A\cup B})=1 - 0.28 = 0.72$.

Step2: Use the formula for $P(A\cup B)$

The formula for the probability of the union of two events is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
We know $P(A\cup B) = 0.72$, $P(A)=0.26$ and $P(B)=0.49$. Substitute these values into the formula:
$0.72=0.26 + 0.49-P(A\cap B)$.

Step3: Solve for $P(A\cap B)$

Rearrange the equation $0.72=0.26 + 0.49-P(A\cap B)$ to get $P(A\cap B)=0.26 + 0.49-0.72$.
$P(A\cap B)=0.03$.

Answer:

A. 0.03