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16 June, 03:23

A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar. Three coins are randomly selected from the jar.

a. List the simple events in S. b. What is the probability that the selection will contain the half-dollar? c. What is the probability that the total amount drawn will equal 60¢ or more?

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  1. 16 June, 03:34
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    a.

    Let N represent Nickel

    D represent Dime

    Q represent Quarter

    H represent Half-Dollar

    E1 = (NDQ)

    E2 = (NDH)

    E3 = (NQH)

    E4 = (DQH).

    Then, S = {E1, E2, E3, E4}

    b. 3/4

    c. 3/4

    Step-by-step explanation:

    a. Simple events are those ones that happens at one time and have a single outcome. If the event is denoted by F, then the probability is denoted by P (F), and is usually between 0 and 1. In this light, the simple events in the above are;

    Let N represent Nickel

    D represent Dime

    Q represent Quarter

    H represent Half-Dollar

    E1 = (NDQ)

    E2 = (NDH)

    E3 = (NQH)

    E4 = (DQH).

    Then, S = {E1, E2, E3, E4}

    b. Probability that the selection will contain the half-dollar = Probability that a nickel, a dime, and a half-dollar is selected + Probability that a nickel, a quarter, and a half-dollar is selected + Probability that a dime, a quarter, and a half-dollar is selected

    P (selection will contain the half-dollar) = P (E2) + P (E3) + P (E4)

    =1/4 + 1/4 + 1/4 = 3/4

    c. Probability that the total amount drawn will equal 60¢ or more

    Nickel (N) = 5 cents

    Dime (D) = 10 cents

    Quarter (Q) = 25 cents

    Half-Dollar (H) = 50 cents

    Hence we look at the simple events and their monetary values:

    E1 = NDQ = 40 cents

    E2 = NDH = 65 cents

    E3 = NQH = 80 cents

    E4 = DQH = 85 cents

    Hence,

    P (total amount is 60 cents or more) = P (E2) + P (E3) + P (E4)

    = 1/4 + 1/4 + 1/4 = 3/4
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