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13 February, 00:52

A gumball dispenser has 38 orange gumballs, 27 purple ones, and 15 yellow ones. The dispenser operates such that one quarter delivers 1 gumball. (a) Using three quarters, what is the probability of obtaining 3 gumballs in the order orange, purple, orange? b) using 1 quarter, what is the probability of obtaining 1 gumball that is either purple or yellow?

c) using 3 quarters, what is the probability that of the 3 gumballs obtained, exactly 1 will be purple and 1 will be yellow?

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  1. 13 February, 01:02
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    Answer:1). 0.077

    2). 0.525

    3). 0.09366

    Step-by-step explanation:

    Total number of balls = 38 orange + 28 purple + 15 yellow = 80 balls.

    1). Probability of 3 balls in order of orange, purple, orange.

    Probability = (38/80) * (27/79) * (37/78)

    =0.475*0.3418*0.474

    = 0.077

    2). Probability of either purple or yellow

    Probability = (27/80) + (15/80)

    = 0.525

    3). Probability of exactly 1 color each in 3 balls

    Probability = 3 ((38*27*15) / (80*79*78))

    = 3 * (15390/492969)

    =3*0.03122

    =0.09366
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