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When an experiment is conducted, events A, B, and C are al
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07 Aug 2020, 09:39
07 Aug 2020, 09:39
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65% (00:45) correct
34% (01:14) wrong based on 97 sessions
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\(0<p<1\)
When an experiment is conducted, events A, B, and C are all independent of one another. Each of events A, B, and C has a probability p of occurring.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
When an experiment is conducted, events A, B, and C are all independent of one another. Each of events A, B, and C has a probability p of occurring.
Quantity A |
Quantity B |
The probability that events A and B occur and event C does not occur |
\(p(1-p)\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Re: When an experiment is conducted, events A, B, and C are al
[#permalink]
07 Aug 2020, 12:24
07 Aug 2020, 12:24
2
Carcass wrote:
\(0<p<1\)
When an experiment is conducted, events A, B, and C are all independent of one another. Each of events A, B, and C has a probability p of occurring.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
When an experiment is conducted, events A, B, and C are all independent of one another. Each of events A, B, and C has a probability p of occurring.
Quantity A |
Quantity B |
The probability that events A and B occur and event C does not occur |
\(p(1-p)\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Kudos for the right solution and explanation
Quantity A can be rewritten as p*p*(1-p) and Quantity B can be rewritten as p-p^2. Choose any value for p between 0 and 1, and B will be greater.
Re: When an experiment is conducted, events A, B, and C are al
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08 Aug 2020, 09:07
08 Aug 2020, 09:07
2
General Rule.
If n events are mutually independent then so are their complements and any combination of them.
that is since A,B,C are independent so are A complement, B complement, C complement and any combination of them
Also for any two independent events X and Y: P(X,Y)=P(x)P(Y)
Therefore we are comparing
P(A,B, C complement) with p(1-p)
Quantity A
=P(A,B, C complement)
=P(A)P(B)P(C complement) (Since they are independent)
=P(A)P(B)(1-P(C))
=p*p*(1-p)
=p*QuantityB
Notice Quantity A is p* Quantity B
p is between 0 and 1.
Whenever we multiply a positive number by a number between 0 and 1 it always makes it smaller
Therefore
p(1-p) is larger than p*p*(1-p)
Final Answer: B
If n events are mutually independent then so are their complements and any combination of them.
that is since A,B,C are independent so are A complement, B complement, C complement and any combination of them
Also for any two independent events X and Y: P(X,Y)=P(x)P(Y)
Therefore we are comparing
P(A,B, C complement) with p(1-p)
Quantity A
=P(A,B, C complement)
=P(A)P(B)P(C complement) (Since they are independent)
=P(A)P(B)(1-P(C))
=p*p*(1-p)
=p*QuantityB
Notice Quantity A is p* Quantity B
p is between 0 and 1.
Whenever we multiply a positive number by a number between 0 and 1 it always makes it smaller
Therefore
p(1-p) is larger than p*p*(1-p)
Final Answer: B
