Respuesta :
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!!!
For the given experiment, the probabilities will be:
- A) P = 0.16
- B) P = 0.64
- C) P = 0.36
- D) P = 0.46
How to find the probabilities?
First, we have two urns, the probability of selecting each urn is 0.5. Then the urns have marbles inside of it, and the probability of getting a marble of a given colour is equal to the quotient between the number of marbles with that color on the urn and the total number of marbles on the urn.
A) The probability of randomly selecting urn 2 is p = 0.5
The probability of getting a white marble is:
p' = 8/(8+17) = 0.32
The joint probability is the product of these two:
P = 0.5*0.32 = 0.16
B) Here we count for both urns, so we add a factor of 0.5 for the probability of selecting the correspondent urns. The probability will be:
P = 0.5*19/(19 + 13) + 0.5*17/(17 + 8) = 0.64
C) Similar approach as above:
P = 0.5*13/(19 + 13) + 0.5*8/(17 + 8) = 0.36
D) For the urn I the probability of getting a violet marble is:
p = 19/(19 + 13) = 0.59
While for urn 2 it is:
q = 17/(17 + 8) = 0.68
So the probability that the urn was selected from urn 1 is:
P = (0.59)/(0.59 + 0.68) = 0.46
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
