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.
Are the two trials independent or dependent? Give reasons to support your answer [2]
Draw a probability tree diagram to show the execution of this random experiment. [2]
What is the probability of drawing a white marble from box B at the end of 2nd trial? [2]
What is the probability of drawing a black marble from box B at the end of 2nd trial? [2]
Identify all the mutually exclusive events present in the given scenario and verify that they
are mutually exclusive. [2]
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.
Answers
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