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Math Help - probability that a randomly chosen member

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    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.
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  2. #2
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    Quote Originally Posted by affelix View Post
    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}<br />

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

    Then read off the required probability.
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