ball is drawn from one of three urns depending on the outcomeof a roll of a dice. If the dice shows a 1, a ball is drawn from Urn I, whichcontains 2 black balls and 3 white balls. If the dice shows a 2 or 3, a ballis drawn from Urn II, which contains 1 black ball and 3 white balls. Ifthe dice shows a 4, 5, or 6, a ball is drawn from Urn III, which contains1 black ball and 2 white balls. (i) What is the probability to draw a black ball? [7 Marks]Hint. Use the partition rule.(ii) Assume that a black ball is drawn. What is the probabilitythat it came from Urn I? [4 Marks]Total marks 11 Hint. Use Bayes’ rule
ball is drawn from one of three urns depending on the outcomeof a roll of a dice. If the dice shows a 1, a ball is drawn from Urn I, whichcontains 2 black balls and 3 white balls. If the dice shows a 2 or 3, a ballis drawn from Urn II, which contains 1 black ball and 3 white balls. Ifthe dice shows a 4, 5, or 6, a ball is drawn from Urn III, which contains1 black ball and 2 white balls. (i) What is the probability to draw a black ball? [7 Marks]Hint. Use the partition rule.(ii) Assume that a black ball is drawn. What is the probabilitythat it came from Urn I? [4 Marks]Total marks 11 Hint. Use Bayes’ rule
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 34T
Related questions
Question
ball is drawn from one of three urns depending on the outcome
of a roll of a dice. If the dice shows a 1, a ball is drawn from Urn I, which
contains 2 black balls and 3 white balls. If the dice shows a 2 or 3, a ball
is drawn from Urn II, which contains 1 black ball and 3 white balls. If
the dice shows a 4, 5, or 6, a ball is drawn from Urn III, which contains
1 black ball and 2 white balls.
(i) What is the
Hint. Use the partition rule.
(ii) Assume that a black ball is drawn. What is the probability
that it came from Urn I? [4 Marks]
Total marks 11 Hint. Use Bayes’ rule
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