Answer:
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
Hope this Helps!!!
