The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and the probability that a randomly sele

Question

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomly selected person is a runner, given that he has high blood pressure.

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2 months 2021-10-09T00:47:33+00:00 1 Answer 0 views 0

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    2021-10-09T00:49:08+00:00

    Answer:

    The probability of choosing a person with BP  who is also a runner is 2/3.

    Step-by-step explanation:

    According to the given data:

    P( Selecting a  person with high blood pressure )  =  0.3

    or, P(H)  = 0.3

    P( Selecting a  person who is a Runner )  =  0.4

    or, P(R)  = 0.4

    Now, P( Randomly Selecting a person who has high BP and is a runner)  = 0.2

    P(H∩ R)  = 0.2

    Now, we need to find the P(randomly selected person is a runner and has already has high BP)

    or we need to find: P(R/H)

    now, by BAYES THEOREM:

    P(R/H) = \frac{P(R\cap H)}{P(H)}

    \implies P(R/H) = \frac{0.2}{0.3 }  =  \frac{2}{3}

    Hence, the probability of choosing a person with BP  who is also a runner is 2/3.

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