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 [2]

b. Draw a probability tree diagram to show the execution of this random experiment. [2]

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

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

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

are mutually exclusive. [2]

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. [2]





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Answer 1

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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