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Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red. Moreover, suppose 9 of the green marbles are opaque, 5 of the blue marbles are opaque, and 3 of the red marbles are opaque, and the rest of the marbles are transparent. Suppose you draw one marble from the bag and let G, B, and R be the events that the marble is green, blue, and red, respectively, and let O be the event that it is opaque. (a) Find P(RO). (b) Find P(RO). (c) Find P(R). (d) Check whether R and O are independent. Find P(BO). (f) Find P(OG). (g) Find P(BUGIO).

Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red. Moreover, suppose 9 of the green marbles are opaque, 5 of the blue marbles are opaque, and 3 of the red marbles are opaque, and the rest of the marbles are transparent. Suppose you draw one marble from the bag and let G, B, and R be the events that the marble is green, blue, and red, respectively, and let O be the event that it is opaque. (a) Find P(RO). (b) Find P(RO). (c) Find P(R). (d) Check whether R and O are independent. Find P(BO). (f) Find P(OG). (g) Find P(BUGIO).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 42E
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5. Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red. Moreover, suppose 9 of the green marbles are opaque, 5 of the blue marbles are opaque, and 3 of the red marbles are opaque, and the rest of the marbles are transparent. Suppose you draw one marble from the bag and let G, B, and R be the events that the marble is green, blue, and red, respectively, and let O be the event that it is opaque. (a) Find P(RO). (b) Find P(R|Oº). (c) Find P(R). (d) Check whether R and O are independent. (e) Find P(BO). (f) Find P(OG). (g) Find P(BUGIO).
Transcribed Image Text:5. Consider a bag of marbles, 19 of which are green, 25 of which are blue, and 6 of which are red. Moreover, suppose 9 of the green marbles are opaque, 5 of the blue marbles are opaque, and 3 of the red marbles are opaque, and the rest of the marbles are transparent. Suppose you draw one marble from the bag and let G, B, and R be the events that the marble is green, blue, and red, respectively, and let O be the event that it is opaque. (a) Find P(RO). (b) Find P(R|Oº). (c) Find P(R). (d) Check whether R and O are independent. (e) Find P(BO). (f) Find P(OG). (g) Find P(BUGIO).
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