6. Let E, F, G be three events. Find expressions for the events that of E, F, G a. only E occurs; b. both E and G but not F occur; c. at lea

Question

6. Let E, F, G be three events. Find expressions for the events that of E, F, G a. only E occurs; b. both E and G but not F occur; c. at least one of the events occurs; d. at least two of the events occur; e. all three occur; f. none of the events occurs; g. at most one of them occurs; h. at most two of them occur; i. exactly two of them occur; j. at most three of them occur.

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Thu Giang 3 days 2021-07-19T20:44:26+00:00 1 Answers 0 views 0

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    2021-07-19T20:46:15+00:00

    Answer:

    a.) only E occurs :

    E((FUG)’)

    b.) both E and G but not F

    EG(F’)

    C.) Atleast one of the events :

    (E U G U F)

    d.) Atleast two of the events

    (EG U EF U GF)

    E.) all three occurs

    (EGF)

    F.) none of the events occur :

    (E U G U F)’

    G.) At most one of the events occur

    (EG U EF U GF)’

    H.) at most two of them occur

    (E’ U G’ U F’)

    I.) exactly two of them occur;

    (EG U EF U GF) * (EGF)’

    j. at most three of them occur.

    EFG U (EFG)’

    Step-by-step explanation:

    Events = {E, F, G}

    a.) only E occurs :

    E((FUG)’) ; E and not F or G

    b.) both E and G but not F

    EG(F’) ; both E and G and not F

    C.) Atleast one of the events :

    (E U G U F) ; Either E or F or G

    d.) Atleast two of the events

    (EG U EF U GF) ; Either EG or EF or GF occurs

    E.) all three occurs

    (EGF) ; All three events, E, G and F occurs

    F.) none of the events occur :

    (E U G U F)’ ; Neither E, G nor F occurs

    G.) At most one of the events occur

    (EG U EF U GF)’ ; complement of atleast two) at most one

    H.) at most two of them occur

    (E’ U G’ U F’) ; Either E , F or G does not occur

    I.) exactly two of them occur;

    (EG U EF U GF) * (EGF)’ ; Exactly two events occurs and all three events Do not occur

    j. at most three of them occur.

    EFG U (EFG)’ ; All three events occur union all three events do not occur

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