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Information given:
- Probability that all penguins complete migration: 0.05
- Each penguin has same probability of completing migration (independent of each other).

Question:
- What is the probability that none of the penguins complete migration?

Solution:
- Let p = probability that one penguin completes migration
- Let n = number of penguins
- Therefore, p^n = 0.05
- Probability that one penguin does not complete migration: (1-p)^n
- We know that p^n = 0.05, but don't know either p or n
- Therefore, (1-p)^n can not be determined from given information

Answer: E, cannot be determined from given information
Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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Answer is D - 0.95. Probability of none = 1 - Probability of all

Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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Probability that all penguins complete migration is 0.05.

Let’s say there are "n" number of penguins and each penguin has a probability "p" of completing the migration. Then the probability that all of them complete it is p^n = (0.05)

But since we don’t know how many penguins there are, we can’t find the probability that no one complete it, which would be (1 - p)^n.

IMO the answer is E
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It is given that P(all penguins complete migration) = 0.05
Each penguin has the same probability of completing the migration. We do not know how many penguins are there.
Let number of penguins be = n
Let probability of each penguin completing the migration = p
This implies that the figure 0.05 comes from p^n.
Both p and n are unknown.
Probability that none complete the migration is (1-p)^n.
Since we do not have the necessary data for evaluating the above probability, the correct answer is E i.e. Cannot be determined from the given information­.
Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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P(none of the penguins completing the migration) = 1 - P(all penguins completing the migration) = 1 - 0.05 = 0.95
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The probability that all penguins migrate is 5/100. Let's say the probability that one migrates is p.
the probability that all migrate = p * p * p * p^n = 0.05.
where n is the no. of penguins.
The probability that none of them goes would be 1 minus the probability that everyone goes.
I.e., (1-p)^n
If the chance of all going is 0.05, and each penguin has a 50% chance of going (like flipping a fair coin), then it turns out:
The chance of all going = 0.5^n
The chance of none going = 0.5^n
So they’re the same.
And since you were told the chance of all going is 0.05, then the chance of none going is also 0.05
Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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Let's assume that there are n penguins and p is the probability of migration.


So according to the information, the Probability that all the n penguins complete their annual migration = \(p^n. \\
\)
What we are asked is the none of the penguins complete the migration = \((1-p)^n. \)

We know \(p^n. \) = 0.05.
We need \((1-p)^n. \), we cannot find this value as there are 2 variables.

n can take 1,2,3... So we cannot determine the probability with the given information.

IMO E
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E. Cannot be determined from the given information­
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The probability that all the penguins complete their migration is 0.05.

Each penguin has the same independent probability (P) of completing the migration. As we don't know how many number of penguins are there, the answer cannot be determined from the information.
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As the sum of all probabilities is 1 so for none of penguins completing it would be individual probablity^no of penguins-1
But there are two unknowns and only 1 equation so not possible to determine based on given data. Option E

Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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Given:
The probability that all penguins in a group complete their migration is 0.05.

Each penguin has the same probability of completing the migration.

Find:
The probability that none of the penguins complete the migration.

Solution:
Assume there is only 1 penguin (since the problem does not specify the number of penguins, but "all" can refer to a single penguin).

If the probability that this one penguin completes migration is 0.05, then:

The probability that it does not complete migration is:

1−0.05=0.95
1−0.05=0.95
Since there’s only one penguin, the probability that none complete migration is the same as the probability that this one penguin fails, which is 0.95.
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Simply there is not enough info to calculate the question i.e. the number of penguins or the probability of completing per penguin
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The probability that all penguins complete = P(all complete) = 0.05

It is given that all penguins have the same rate of completion. Let the number of penguins be n.

Probability of completion = P(completion)

P(all complete) = P(completion)^n

Probaility of not completing = P(no completion) = 1−P(completion)

Probability that none of the penguins complete = P(none complete) = (P(no completion))^n = (1−P(completion))^n

Since n is not known, it is not possible to find the solution.

Ans. E
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Value of total number of pengiuns are required to find the required answer.
Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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E) Can not be determined.

Explanation:
Let there be n penguins.
Chance that all of them complete the migration is
P(all)=p^n=0.05.

But the chance that none complete is
P(none)=(1−p)^n

without n we can't determine the probabiliy.
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We are told that the probability that all the penguins in a study group complete their annual migration is 0.05, and that each penguin has the same chance of completing the migration. However, we are not told how many penguins are in the group or what the individual probability is for one penguin to complete the migration. Without knowing either the number of penguins or each penguin’s individual success rate, we cannot calculate the probability that none of them complete the migration. Different combinations of individual probabilities and group sizes could result in the same 0.05 probability for all completing the migration, but would give different results for the chance that none complete it. Therefore, the probability that none of the penguins complete the migration cannot be determined from the given information.
Answer: E. Cannot be determined from the given information.
Bunuel
The probability that all the penguins in a marine study group complete their annual migration is 0.05. If each penguin has the same probability of completing the migration, what is the probability that none of the penguins complete the migration?

A. 0.05
B. 0.5
C. 0.75
D. 0.95
E. Cannot be determined from the given information­


 


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for the GMAT Club Olympics Competition

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answer is E
we don't know how many p in the group
the none of p(P) is 1-0.05^n
n is not given in the information
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