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3 April, 02:36

A convenience store has made up 20 grab bag gifts and is offering them for $3 a bag. 9 bags contain merchandise worth 50 cents. Eights bags contain merchandise $2.25, and three bags contain merchandise worth $5. Suppose you purchase one bag, what is your expected gain or loss?

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Answers (2)
  1. 3 April, 05:12
    0
    Expected loss = $-1.13

    Step-by-step explanation:

    9 bags contain merchandise worth $0.50

    8 bags contain merchandise worth $2.25

    3 bags contain merchandise worth $5

    Total bags are 20

    $0.50 * (9/20) + $2.25 * (8/20) + $5 * (3/20)

    $0.225 + $0.9 + $0.75

    $1.87

    The cost of bag is $3

    The expected value is

    E = $1.87 - $3

    E = $-1.13 (this is a loss)

    So you are most likely to lose $1.13 if you purchase 1 bag at the convenience store.
  2. 3 April, 06:16
    0
    Probability of selecting a bag contain merchandise worth 50 cents is 9/20 = 0.45

    Probability of selecting a bag contain merchandise worth $2.25 is 8/20 = 0.4

    Probability of selecting a bag contain merchandise worth $5 is 3/20 = 0.15

    Expected gain/loss = 0.45*9 + 0.4*8 + 0.15*3 - 3 = 4.05+3.2+0.45 - 3 = 4.7

    Hence there is expected gain of 4.7
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