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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribe the following text in digital format please
![Posic
□ To show :-
Goto
P(AUB) = P(A)+R(B) -P(ARB)
Proofis
Since A & B are any two events have not
disjoint
(AUB) event composed of three mutually exclusi
exclusive events. (ANB'), (ANB) & (BOB)
L. By Axiom (A3)
P(AUB)
P(ANB) +P (ADB) + P(A²DB)
Similarly," P(A) = PLANB') +P(ANB)
Similarly,.. P(B) = P(ANB) + P(A'OB)
Adding TE & TT
PLAY+PCB) = PLANB') +P(ANB) + D (ANB) +P(AMB)
= P(AUB) +P(ANB)
from
!
P(AUB) = P(A) + P (B) -P(ANB)
3
To show :~ P(AUBUC) = P(A) + P(B)+PCC) - PLANB)
- P(BOC) -PCAO.C) +P CAN BNC)
Proof:- bet (BUC) = 0
~P(AUBUC) = P(AUD)=P(A2+R(D)=P(AND)
•· P(A) + P(BUC) - P(AN (BUC)]
=
• P(A) + P(BUC) - P((ANB)U(ANC)]
= P(A) +P(B) +PCC) - P(BOC) - [P(ADB) +P(ANC)
[P(ADBDC)]
PEAAB PLAUBUC) = P(A) + P(B) + PCC) - P(ANB)
-P(BOC) - PIANS) +PCAMBO)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72bef688-d82f-442d-8d89-07358c129e0a%2F514e41f1-50bd-4402-b597-68ca1d8135b1%2Ftl7xyo_processed.png&w=3840&q=75)
Transcribed Image Text:Posic
□ To show :-
Goto
P(AUB) = P(A)+R(B) -P(ARB)
Proofis
Since A & B are any two events have not
disjoint
(AUB) event composed of three mutually exclusi
exclusive events. (ANB'), (ANB) & (BOB)
L. By Axiom (A3)
P(AUB)
P(ANB) +P (ADB) + P(A²DB)
Similarly," P(A) = PLANB') +P(ANB)
Similarly,.. P(B) = P(ANB) + P(A'OB)
Adding TE & TT
PLAY+PCB) = PLANB') +P(ANB) + D (ANB) +P(AMB)
= P(AUB) +P(ANB)
from
!
P(AUB) = P(A) + P (B) -P(ANB)
3
To show :~ P(AUBUC) = P(A) + P(B)+PCC) - PLANB)
- P(BOC) -PCAO.C) +P CAN BNC)
Proof:- bet (BUC) = 0
~P(AUBUC) = P(AUD)=P(A2+R(D)=P(AND)
•· P(A) + P(BUC) - P(AN (BUC)]
=
• P(A) + P(BUC) - P((ANB)U(ANC)]
= P(A) +P(B) +PCC) - P(BOC) - [P(ADB) +P(ANC)
[P(ADBDC)]
PEAAB PLAUBUC) = P(A) + P(B) + PCC) - P(ANB)
-P(BOC) - PIANS) +PCAMBO)
Expert Solution
Step 1
Introduction:
The set of all the elements that are either in A or in B is the union of the two sets A and B, or A B, whereas the set of all the elements that are common is the intersection of the two sets A and B. stands for the intersection of these two sets.
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