a student takes two subjects A and B. Know that the probability of passing subjects A and B is 0.8 and 0.7 respectively. If you have passed

Question

a student takes two subjects A and B. Know that the probability of passing subjects A and B is 0.8 and 0.7 respectively. If you have passed subject A, the probability of passing subject B is 0.8. Find the probability that the student passes both subjects? Find the probability that the student passes at least one of the two subjects

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Amity 4 years 2021-08-06T21:32:11+00:00 1 Answers 28 views 0

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  1. Ben
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    2021-08-06T21:33:59+00:00
    Reply

    Answer:

    0.64 = 64% probability that the student passes both subjects.

    0.86 = 86% probability that the student passes at least one of the two subjects

    Step-by-step explanation:

    Conditional Probability

    We use the conditional probability formula to solve this question. It is

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    In which

    P(B|A) is the probability of event B happening, given that A happened.

    P(A \cap B) is the probability of both A and B happening.

    P(A) is the probability of A happening.

    In this question:

    Event A: Passing subject A

    Event B: Passing subject B

    The probability of passing subject A is 0.8.

    This means that P(A) = 0.8

    If you have passed subject A, the probability of passing subject B is 0.8.

    This means that P(B|A) = 0.8

    Find the probability that the student passes both subjects?

    This is P(A \cap B). So

    P(B|A) = \frac{P(A \cap B)}{P(A)}

    P(A \cap B) = P(B|A)P(A) = 0.8*0.8 = 0.64

    0.64 = 64% probability that the student passes both subjects.

    Find the probability that the student passes at least one of the two subjects

    This is:

    p = P(A) + P(B) - P(A \cap B)

    Considering P(B) = 0.7, we have that:

    p = P(A) + P(B) - P(A \cap B) = 0.8 + 0.7 - 0.64 = 0.86

    0.86 = 86% probability that the student passes at least one of the two subjects

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