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18 July, 05:48

a fair die is tossed. A is the event that the outcome is odd. B is the event that the outcome is even. C is the event that the outcome is ess than 4.

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  1. 18 July, 06:01
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    The question is incomplete. Below is the complete question

    "A fair die is tossed. A is the event that the outcome is odd. B is the event that the outcome is even. C is the event that the outcome is less than 4. Determine P (A), P (B), P (C), P (A∩B), P (B∩C), P (A|B), P (A|C), P (B|C).

    answers:

    a. 1/2

    b. 1/2

    c. 1/2

    d. 0

    e. 1/6

    f. 0

    g. 2/3

    h. 1/3

    Step-by-step explanation:

    lets write out the probability of each event

    a. A=outcome is odd

    A={1,3,5}

    P (A) = 1/2

    b. B=outcome is even

    B={2,4,6}

    P (B) = 1/2

    c. C=outcome is less than 4

    C={1,2,3}

    P (C) = 1/2

    d. P (AnB) = {its odd and even i. e what is common between set A and B}

    Therefore, P (AnB) is a null set i. e P (AnB) = { }=0

    e. BnC = {2} i. e elements common between set B and C

    Hence P (BnC) = 1/6

    f. PA = P (AnB) / P (B) since P (AnB) = 0, P (B) = 1/2. then, P (A|B) = 0

    g. P (A|C) = P (AnC) / P (C) since P (AnC) = 1/3, P (C) = 1/2. therefore, P (A|C) = 2/3

    h. P (B|C) = P (BnC) / P (C), since P (BnC) = 1/6, P (C) = 1/2. therefore, P (B|C) = 1/3
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