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 Draw a probability tree diagram to show the execution of this random experiment. What is the probability of drawing a white marble from box B at the end of 2nd trial? What is the probability of drawing a black marble from box B at the end of 2nd trial? Identify all the mutually exclusive events present in the given scenario and verify that they are mutually exclusive. 6. 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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
- Draw a
probability tree diagram to show the execution of this random experiment. - What is the probability of drawing a white marble from box B at the end of 2nd trial?
- What is the probability of drawing a black marble from box B at the end of 2nd trial?
- Identify all the mutually exclusive
events present in the given scenario and verify that they are mutually exclusive. 6. 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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