Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B.

 

Answer the following questions.

 

a. Are the two trials independent or dependent? Give reasons to support your answer?

b. Draw a probability tree diagram to show the execution of this random experiment. ?

c. What is the probability of drawing a white marble from box B at the end of 2nd trial? 

d. What is the probability of drawing a black marble from box B at the end of 2nd trial? 

e. Identify all the mutually exclusive events present in the given scenario and verify that they are mutually exclusive ?

f. If we reverse the scenario, then what is the probability of drawing a black marble from box A given that a white marble is drawn from box B.?

 

 

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