# Math Help - probability that a randomly chosen member

1. ## probability that a randomly chosen member

Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist. Determine the probability that a randomly chosen member of this group visits a physical therapist.

2. Originally Posted by affelix
Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist. Determine the probability that a randomly chosen member of this group visits a physical therapist.
Complete the following Karnaugh Table:

$\begin{tabular}{l | c | c | c} & P & P' & \\ \hline C & 0.22 & a & 0.22 + a \\ C' & b & 0.12 & b + 0.12 \\ \hline & 0.22 + b & a + 0.12 & 1 \\ \end{tabular}
$

subject to the condition (0.22 + a) - (0.22 + b) = 0.14.

Then read off the required probability.