Question

The chances that a visit to a primary health centre (PHC) results in neither lab work, nor referred to a specialist is 35%. Out of those coming to a PHC, 30% are referred to a specialist, and 40% require lab work. Find the probability that a visit
to a PHC results in both lab work and referral to a specialis.

Answer 1

Answer on Question #86255 – Math – Statistics and Probability

Question

The chances that a visit to a primary health centre (PHC) results in neither lab work, nor referred to a specialist is 35%. Out of those coming to a PHC, 30% are referred to a specialist, and 40% require lab work. Find the probability that a visit

to a PHC results in both lab work and referral to a specialist.

Solution

Denote

$A =$ ‘lab work’, $B =$ ‘referred to a specialist’

We have:

$$P(\bar{A} \cap \bar{B}) = 0.35, P(A) = 0.3, P(B) = 0.4$$

By inclusion exclusion formula

$$\begin{array}{l} P(A \cap B) = P(A) + P(B) - P(A \cup B) = \\ = P(A) + P(B) - \left(1 - P(\bar{A} \cap \bar{B})\right) = \\ = 0.3 + 0.4 - (1 - 0.35) = 0.05 \\ \end{array}$$

Answer: 0.05.

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