An experiment consists of selecting one of two urns and then removing a marble from the urn. Urn I contains 19 violet marbles and 13 white marbles. Urn II contains 17 violet marbles and 8 white marbles. Assume that the urns are equally likely to be selected. Find the probability that: A. Urn II and a white marble are selected. B. A violet marble is selected. C. A white marble is selected. D. A marble was selected from Urn I, if it is known that the marble is violet.

A) (4/25) = 0.16

B) 0.636875

C) 0.363125

D) 0.4661

Step-by-step explanation:

Urn I contains 19 violet marbles and 13 white marbles.

Urn II contains 17 violet marbles and 8 white marbles.

A. Urn II and a white marble are selected.

Probability of selecting Urn II = (1/2)

Probability of selecting a white marble from urn II = (8/25)

Probability of picking urn II and selecting a white marble = (1/2) × (8/25) = (4/25) = 0.16

B. A violet marble is selected.

Probability of selecting a violet marble is a sum of the probability of selecting a violet marble from urn I and probability of selecting a violet marble from urn II

Probability of selecting a violet marble from urn I = (1/2) × (19/32) = 0.296875

Probability of selecting a violet marble from urn II = (1/2) × (17/25) = 0.34

Probability of selecting a violet marble

= (0.296875) + (0.34) = 0.636875

C. A white marble is selected.

Probability of selecting a white marble is a sum of the probability of selecting a white marble from urn I and probability of selecting a white marble from urn II

Probability of selecting a white marble from urn I = (1/2) × (13/32) = 0.203125

Probability of selecting a white marble from urn II = (1/2) × (8/25) = 0.16

Probability of selecting a white marble

= (0.203125) + (0.16) = 0.363125

D. A marble was selected from Urn I, if it is known that the marble is violet.

Probability of selecting a violet marble = 0.636875 (from part B)

Probability of selecting a violet marble from urn I = (1/2) × (19/32) = 0.296875

Probability of selecting marble was selected from Urn I, if it is known that the marble is violet = (0.296875/0.636875) = 0.4661

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