Assume you have two boxes An and B. Box A contains 7 dark marbles, 4 white marbles. Box B contains 7 white and 4 dark marbles. An arbitrary investigation is acted in two consecutive preliminaries by first drawing a marble arbitrarily from enclose An and putting to Box B. In the second preliminary after the primary preliminary, a marble is drawn arbitrarily from box B.

Answer the accompanying inquiries.

a. Are the two preliminaries free or ward? Offer motivations to help your response

b. Draw a likelihood tree graph to show the execution of this arbitrary trial.

c. What is the likelihood of drawing a white marble from box B toward the finish of second preliminary?

d. What is the likelihood of drawing a dark marble from box B toward the finish of second preliminary?

e. Recognize every one of the totally unrelated occasions present in the given situation and confirm that they

are totally unrelated.

f. On the off chance that we turn around the situation, what is the likelihood of drawing a dark marble from

box A given that a white marble is drawn from box B.

One understudy applies for a doctoral program in Economics. The capability of the affirmation relies upon GRE score, GPA in his undergrad and graduate schools, three proposal letters, and other steady documentations. Since this is a top program and a top college in the United States, complete number of candidates is 750, however this program just concedes 25 understudies each year. Along these lines, this understudy asserts that he has 3.3% likelihood to be conceded. Does this current understudy's case bode well? Why or why not? Talk about and clarify your reasons. You should give your measurable investigation and reasons.

Assume in a class there are 170 understudies. Of those 170 understudies, 90 are guys and 80 are females. Among 90 male understudies, 55 like playing the sport of football, and 35 don't care for it. Among 80 female understudies, 10 like playing the sport of football, and 70 don't care for it.

Address this data as a cross-classification or likelihood possibility table.

Show likelihood tree charts for every one of the conceivable irregular occasions that can happen (with their probabilities) if an understudy is picked haphazardly in this class.

(4)

Assume you have two boxes An and B. Box A contains 7 dark marbles, 4 white marbles. Box B contains 7 white and 4 dark marbles. An arbitrary trial is acted in two consecutive preliminaries by first drawing a marble arbitrarily from enclose An and putting to Box B. In the second preliminary after the main preliminary, a marble is drawn haphazardly from box B.

Answer the accompanying inquiries.

d. What is the likelihood of drawing a dark marble from box B toward the finish of second preliminary?

e. Distinguish every one of the totally unrelated occasions present in the given situation and confirm that they are totally unrelated ?

f. Assuming we switch the situation, what is the likelihood of drawing a dark marble from box A given that a white marble is drawn from box B.?