GMAT Club Olympics 2025 (Day 1): The probability that all the penguins : Problem Solving (PS)

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Bunuel

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30 Jun 2025, 08:00

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Bunuel

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30 Jun 2025, 08:30

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Bunuel

GMAT Club Official Explanation:

We are told the probability that all penguins complete the migration is 0.05. The opposite event is that not all complete it, which has probability 1 - 0.05 = 0.95. But "not all complete" means at least one fails to complete, which is not the same as none complete it.

On the other hand, the probability that none complete it equals P(one penguin does not complete)^(number of penguins) = (1 - P(one penguin completes))^(number of penguins). That, in turn, depends on knowing both the individual probability that a single penguin fails to complete the migration and the total number of penguins. Since we are only told the probability that all complete it, we cannot determine the probability that none do.

Answer: E.

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30 Jun 2025, 08:04

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Cannot be determined from the given information

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E. We cannot figure out the probability that none complete: Probability none complete =1-p)^n, but p and n are both unknown. We just know p^n=0.05

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30 Jun 2025, 08:08

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probability
1 - 0.05 = 0.95

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The answer would be E, because the only information we can get from the stem is probability that not all the penguin complete their anual migration.

P(not all the penguins) = 1 -P(all the penguins)

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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?

Let the probability that a penguin completes the migration be p and there are n penguins in the Marine study group.

The probability that all the penguins in a marine study group complete their annual migration = $p^n = 0.05$
$p = (.05)^(1/n)$

The probability that none of the penguins complete the migration =$ (1-p)^n = (1 - (.05)^(1/n) ) ^n $

The probability depends on the value on n and cannot be determined from the given information.

IMO E

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In this question, the key is to notice that, without the number of penguins, we can not determinar the probability.

If there have only 1 penguin, than the probability will be 1 - 0.05 = 0.95 (this is an instance of the scenario below, where n = 1)

If there have multiples penguins, the probability will be the complementary probability of each sucess powered to the n-th power, where n is the number of penguins.

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30 Jun 2025, 08:10

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Let p be a single penguin's probability of completing the migration and n be the number of penguins.

The probability of all n penguins succeeding is p^n = 0.05.

The probability of all n penguins failing is (1 - p)^n.

The value of (1 - p)^n depends on the number of penguins (n), which is unknown.

If n = 1: The probability of failure is (1 - 0.05)^1 = 0.95.

If n = 2: The probability of failure is (1 - sqrt(0.05))^2, which is approximately 0.60.

Since the answer changes based on information not provided, a single solution cannot be found.

The correct answer is E. Cannot be determined from the given information.

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Since the combined probability of all penguins = 0.05 & if we assume there are n penguins with equal probability p,

p^n=0.05
p=0.05^(1/n) - (1)

Now to calculate the probability of none of the penguins being able to complete the migration, we can formulate it as (1-p)^n - (2)

Now if we substitute the value of p from 1 in 2, we get:

(1-0.05^(1/n)) ^n

Here we do not know the value of n & hence we cannot find the solution, hence the answer to this question is option (E) Cannot be determined from the given information

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30 Jun 2025, 08:11

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Let P^n be 0.05 (the penguins, who have probablity, complete annual migration),
where p is probability per penguin,
what we require would be (1-p)^n would simply could not be calculated due to lack of data.

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To solve this problem, I need to determine if we can find the probability that none of the penguins complete their migration based on the given information.
The key issue here is that we don't know how many penguins are in the study group. Without knowing the number of penguins, we cannot calculate the individual probability for each penguin, which would be needed to determine the probability that none complete the migration.
Let's say there are n penguins in the group, and the probability of each penguin completing the migration is p.
Given information: The probability that ALL penguins complete the migration is 0.05.
This means: p^n = 0.05
To find the probability that NONE of the penguins complete the migration, we would need to calculate (1-p)^n.
However, without knowing the value of n (the number of penguins), we cannot solve for p from the equation p"n = 0.05, and consequently, we cannot determine (i-p)n.
Therefore, the answer is E. Cannot be determined from the given information

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Probability that all of the penguins completed their migration = 0.05
To find the probability that none of the penguins have completed their migration, we need to subtract the probability that at least one penguin has completed its migration from 1.
P[none of the penguins have completed their migration] = 1- P[atleast 1 penguin has completed its migration]

All penguins have the same probability of completing their migration.
Let the probability of one penguin completing their migration= x
Let the number of penguins= n
$x^n=0.05$
we don't know x or n
We don't have enough information to find the P[atleast 1 penguin has completed its migration]

[E]

Bunuel

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Bunuel

This question was provided by GMAT Club
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Probability of completing the migration = p

Probability of not completing the migration = 1 - p

Given: p^n = 0.05

Asked (1-p)^n ?

As we have two variables and one equation we cannot find the value of p and n. We need more information to answer this question.

Option E

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E. Cannot be determined from the given information

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Let's assume there are "n" penguins, and the probability that each completes its migration is "p"

Then the probability that all penguins complete their migration is given by: $ p^n $, which is given to us as 0.05

So, equation 1 is $p^n $ = 0.05

Now, the probability that each penguin does not complete its migration is given by 1-p

Hence, for "n" penguins, the probability becomes $(1-p)^n $

This is the expression we need to find the value for. However, we only have 1 equation and both "p" and "n" are unknowns, so the answer to this question is:

E. Cannot be determined from the given information

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30 Jun 2025, 08:16

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Answer should be D. Since the probability of all the penguins completing their annual migration is given (0.05). Hence, the the probability that none of the penguins complete the migration will be 1 - 0.05 = 0.95.

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Bunuel

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Answer is E
Prob that none of the penguins complete the migration =1-.05^n

Here we don't know n so E

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30 Jun 2025, 08:18

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Let the number of penguins be n and probability that a penguins completes the annual migration be p
P(all the penguins in a marine study group complete their annual migration) = p^n = 0.05
P(none of the penguins complete the migration) = (1-p)^n
We do not have enough info to calculate this as number of penguins is unknown

Bunuel

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30 Jun 2025, 08:19

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The probability of an event to happen is 0.05 and the probability for that event not to happen is 1 - P(E) i.e 1-0.05 but we are not sure how many penguins are in the pool hence as n is not known it cannot be determined