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605-655 Level|   Probability|         
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 22:13
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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
Let us assume that probability of completing the migration for each penguin is P, and there a total of N penguins.

Therefore, it's given that P^N = 0.05

Now, we have to find the probability that none of the penguins complete the migration.

Which means = probability of each penguin not completing the migration ^ number of penguins

= (1-P)^n

From the given info, this can't be determined.
Hence, the answer is (E)
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 22:18
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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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we don’t know p or n.
For example:
  • If there’s only 1 penguin, then p=0.05p = 0.05p=0.05 and P(none)=1−0.05=0.95
So, the answer depends on n, which is not given.
Therefore, E. Cannot be determined from the given information.
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 22:23
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P(All completing migration) = 0.05
P(Individual completing migration) = p

P(All completing migration) = p^n = 0.05

P(None completing migration) = (1-p)^n

Without the values of p or n we cannot calculate the Probability
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 22:36
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P(All complete) = 0.05.

The question asks us to find P(None complete) = 1 - P(at least one completes)

Since "P(at least one completes)" is not given, it is not possible to find the question.

P.S. Using "1 - 0.05" is actually "1 - P(All complete) = P(Not all complete)"

Not all complete is not the same as None complete.
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:06
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We Don't Know the total number of penguins, we just know probability of whole group migrating lets say probability of one penguin migrating is K and total penguins are N

we can infer: (K)(K)(K)(K).....(K)n = 0.05

But we need to fined (1-K)(1-K)(1-K).....(1-K)n = ?.

Which is not possible without knowing values of K and N

Hence, E. Cannot be determined from the given information
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:11
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We need the the no of penguins to find the exact figure. let x be probability for 1 penguin to succeed and n be no of penguins. so P(all penguin succeed)=(x)^n =0.05

so x(probability for 1 penguin to succeed)=0.05^1/n
now,
p'(none of the penguin succeed)=(1-x)^n= (1- (0.05)^1/n)^n
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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:33
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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

I don't think that the prompt provide enough information to make a choice.
I thought about this in 2 ways:
1. P (0 penguins complete) + P (all penguins) + P (between 0 and all penguins) = 1
We are only given P (all penguins), but do not have information on ways to calculate P (between 0 and all penguins), or the probability where between 0 and all penguins, exclusive, complete the migration

2. if we call p = probability of 1 penguin completing a migration
Then p^n = 0.05 => p = nth root of 0.05
and (1-p)^n = 0.05 => (1-p)^n = (1-nth root of 0.05)^n

Don't have enough information about n or p to solve. Choose E
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:34
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P(E) = 0.05 (given)
We need to find the probability when the event does not occur, P(E')

P(E') = 1-P(E)
P(E') = 1-0.05 = 0.95
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:37
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We are told that the chance of all the penguins finishing their migration is 0.05.

Each penguin has the same chance of making it, but we are not told how many penguins are in the group.

To find the chance that none of them make it, we need to know how many penguins there are.

Since that number is not given, we don't have enough information to find the answer.
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:43
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I would say answer is E. Because they need to give the info about probability of each penguin completing the migration.

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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:56
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Let p be the probability that a single penguin completes the migration.

Let n be the number of penguins.

Then:

Probability that all n penguins complete migration = p^n = 0.05

Probability that none of them complete migration = (1 – p)^n

Now the question: Can we find (1 – p)^n given only p^n = 0.05?

No, we cannot, because we don’t know n or p.

Answer: E. Cannot be determined from the given information

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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 30 Jun 2025, 23:58
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The probability that one penguin complete migration = p
Let total number of penguins be 'n'
The probability that all penguins complete migration = p^n = 0.05
The probability that none complete migration = (1 - p)^n
Since we don’t know the value of p or n, we can’t compute (1 - p)^n
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 00:02
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The probability that all the penguins complete their migration is 0.05.

Let:
• p = the probability that one penguin completes the migration.
• n = number of penguins in the group.

Then:

p^n = 0.05 \tag{1}

We are asked to find the probability that none of the penguins complete the migration.

That is:
(1 - p)^n \tag{2}

Now, can we calculate this?

We only have equation (1), which tells us p^n = 0.05. But we don’t know either p or n individually. Without knowing either the individual probability or the number of penguins, we cannot uniquely compute (1 - p)^n.

Therefore, the correct answer is:

E. Cannot be determined from the given information.
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 00:13
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E. Cannot be determined from the given information­

We need to know the number of penguins to be able to solve this question.
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 00:14
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I chose E, insufficient information present, because we do not have the number of penguins present.

Using complement rule in probability : P(no penguins) + P(atleast one penguin) =1
we can find P(no penguins) if we know P(atleast one penguin), but we only have P(all penguins)
P(atleast one penguin) will be >> P(all penguins)

Algebraic way:
Let's say we have n penguins, each having equal probability, p, of completing migration.
>> P(all penguins completing) = p^n= 0.05
>> p = 0.05^(1/n)

Now P(no penguin completing) =(1-p) ^n = (1-0.05^(1/n)) ^n
there is no way to solve this without knowing n
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 00:30
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And E - cannot be determined because probability of none completing will depend on the number of penguins which we do not have
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 01:07
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D

P(A) = 0.05
P(A)' = 1 - P(A) = 0.095
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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 01:23
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P(None complete the migration) = Total Prob - P(All complete the migration)
= 1 - 0.05 = 0.95
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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 01:59
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Probability to complete migration P(A)= 0.05

Since it is given "all", we will not consider individual numbers.

Let us consider the probability that none of the penguins complete the migration as P(A').

Now, using these values in the formula :


P(A') = 1 - P(A) [ The probability of the complement of event A (not A) is 1 minus the probability of A ]

We get,

P(A')= 1- 0.05 =0.95 (OPTION D)

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


 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 

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GMAT Club Olympics 2025 (Day 1): The probability that all the penguins 01 Jul 2025, 02:24
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The probability that all the penguins complete their migration is 0.05.

Each penguin has an equal, independent chance of migrating successfully.

Let’s assume the probability that one penguin completes the migration is p. If there are n penguins, then:

The probability that all migrate successfully = p^n = 0.05

Now the question asks:

What’s the probability that none of the penguins complete the migration?

That would be the probability that each penguin fails (1−p)^n

But since we don't know p or n, we cannot directly compute
. There are many combinations of p and n that would satisfy
Correct answer: E. Cannot be determined from the given information
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