P4 . There are 100 bottles of sparkling water Pschitt in

convenience store AllinHere. 40 bottles are from Plant A, and the remaining from Plant B. The

level of water in bottles from Plant A is between 0.98 and 1.02 liters versus 0.96 and 1.04 liters

for the bottles from Plant B.

A customer randomly picks one bottle of Pschitt in the convenience store. The level of water

seems to lie between 0.99 and 1 liter. From experiences, it is estimated that 25% of the bottles

from Plant A have a level of water between 0.99 and 1 liter, versus 12.5% for those from Plant

B.

(a) (6 marks) Draw the tree diagram corresponding to the following events:

O = The level of water in the selected bottle lies in the interval [0.99, 1.00] liter; and

N = The level of water in the selected bottle does not lie in the interval [0.99,

1.00] liter. Indicate the corresponding probabilities on each branch of the tree.

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(b) Calculate the probability of the event O.

(c) If event O has been realized, what is the probability that the selected bottle is

from Plant A?

(d) If the observed level of water in the selected bottle is between 1.02 and 1.04

liters, what is the probability that the bottle is from Plant A?