Question

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.

​

Answer 1

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Answer 2

Given :   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.

To Find : 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?

Solution:

Box A   -

B- 7

W -4

Box B

B  - 4

W - 7

Probability of Black from Box A = 7/11    & White = 4/11

Probability of Black from Box B = 4/11    & White = 7/11

After trial 1

Black from Box   A  (7/11)

then Box B  - B  = 5   & W = 7

White from Box   A  (4/11)

then Box B  - B  =4   & W = 8

probability of drawing a black marble from box B

Black from Box  B  =   (7/11) *(5/12)  +  ( 4/11)(4/12)

= (35 + 16)/132

= 51/132

probability of drawing a white marble from box B

White from Box  B  =   (7/11) *(7/12)  +  ( 4/11)(8/12)

= (49 + 32)/132

= 81/132

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