Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) < P(B). [Hint: For such A and B, A and BNA' are disjoint and B = A U (B N A'), as can be seen from a Venn diagram.] Since A is contained in B, we may write B as -Select--- Then P(B) = -Select--- it follows that P(B) 2 --Select-- v, the union of two mutually exclusive events. v. Then, since --Select-- v and P(B) = ---Select-- . This proves the statement.
Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) < P(B). [Hint: For such A and B, A and BNA' are disjoint and B = A U (B N A'), as can be seen from a Venn diagram.] Since A is contained in B, we may write B as -Select--- Then P(B) = -Select--- it follows that P(B) 2 --Select-- v, the union of two mutually exclusive events. v. Then, since --Select-- v and P(B) = ---Select-- . This proves the statement.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) S P(B). [Hint: For such A and B,
A and BNA' are disjoint and B = AU (BN A'), as can be seen from a Venn diagram.]
Since A is contained in B, we may write B as -Select---
Then P(B) = ---Select---
it follows that P(B) 2 --Select- v. This proves the statement.
the union of two mutually exclusive events.
v and P(B) = --Select--
. Then, since ---Select--
For general A and B, what does this imply about the relationship among P(A N B), P(A) and P(A U B)?
O P(A) S P(A N B) S P(A U B)
O P(A N B) S P(A U B) S P(A)
O P(A U B) S P(A N B) S P(A)
O P(A N B) S P(A) S P(A U B)
O P(A) S P(A U B) S P(A N B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2F3a4fb755-d4b9-487c-9473-8cdd8f115753%2Fhrqxlfp_processed.png&w=3840&q=75)
Transcribed Image Text:Show that if one event A is contained in another event B (i.e., A is a subset of B), then P(A) S P(B). [Hint: For such A and B,
A and BNA' are disjoint and B = AU (BN A'), as can be seen from a Venn diagram.]
Since A is contained in B, we may write B as -Select---
Then P(B) = ---Select---
it follows that P(B) 2 --Select- v. This proves the statement.
the union of two mutually exclusive events.
v and P(B) = --Select--
. Then, since ---Select--
For general A and B, what does this imply about the relationship among P(A N B), P(A) and P(A U B)?
O P(A) S P(A N B) S P(A U B)
O P(A N B) S P(A U B) S P(A)
O P(A U B) S P(A N B) S P(A)
O P(A N B) S P(A) S P(A U B)
O P(A) S P(A U B) S P(A N B)
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