If A1, A2, ... , A, are exhaustive and mutually exclusive events associated with a random experiment such that P(A; occurs) = P;, where p, + P2 + if the experiment is repeated n times, then the probability that A, occurs r¡ times, A2 occurs r, times, + Pk = 1, and .... Ag occurs r times is given by .... n! p{1x p2" ... P* .... where r + r2 + ... + rk =n.
If A1, A2, ... , A, are exhaustive and mutually exclusive events associated with a random experiment such that P(A; occurs) = P;, where p, + P2 + if the experiment is repeated n times, then the probability that A, occurs r¡ times, A2 occurs r, times, + Pk = 1, and .... Ag occurs r times is given by .... n! p{1x p2" ... P* .... where r + r2 + ... + rk =n.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Prove the theorem
![If A1, A2, ... , Ag are exhaustive and mutually exclusive events associated with a
random experiment such that P(A; occurs) = pP;, where p, + P2 + ...
if the experiment is repeated n times, then the probability that A, occurs r¡ times,
A2 occurs r, times,
+ Pk = 1, and
%3|
1
Ar occurs r, times is given by
•.•)
n!
rk
Pk
r2
Pi
P„(r], r2>
r):
r!r!..!
...
•..
where
rị + r2 + ... + ry = n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49946af4-f522-49e2-b597-b140ee228d58%2F6ca0bd90-daee-4b81-ae44-677dd00c4a09%2Fcbppppq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If A1, A2, ... , Ag are exhaustive and mutually exclusive events associated with a
random experiment such that P(A; occurs) = pP;, where p, + P2 + ...
if the experiment is repeated n times, then the probability that A, occurs r¡ times,
A2 occurs r, times,
+ Pk = 1, and
%3|
1
Ar occurs r, times is given by
•.•)
n!
rk
Pk
r2
Pi
P„(r], r2>
r):
r!r!..!
...
•..
where
rị + r2 + ... + ry = n.
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