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

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bebu24

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01 Jul 2025, 02:38

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Let there be n penguins and the probability for each penguin to complete the migration be p.
Now it is given in the question that, "the probability that all the penguins in a marine study group complete their annual migration is 0.05", which means:
p^n = 0.05.

IMO, we cannot derive the values of p and n from this.

what is being asked is " the probability that none of the penguins complete the migration?", which translates to:
(1-p)^n

Since we do not know the values of p and n, the answer should be 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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01 Jul 2025, 02:41

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Let the probability that a single penguin completes the migration= p
And number of penguins= n

So, probability that all penguins complete migration = p^n = 0.05.
Then probability that none complete the migration = (1 - p)^n.

Since we don't know p or n, we cannot determine (1 - p)^n (or probability that none complete the migration).

Answer: E. Cannot be determined from the given information.

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01 Jul 2025, 02:42

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The answer is E. Since we don't know the number of penguins

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01 Jul 2025, 02:58

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None (probability that none) = 1-(probability that all)
1-0.05 = 0.95
Ans D

Bunuel

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Bunuel

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Probability that none of the penguins complete the migration + Probability that all of the penguins complete the migration + Probability that some of the penguins complete the migration and remaining did not (All possible combinations) = 1

Information to calculate the Probability that some of the penguins complete the migration and remaining did not (All possible combinations) is not available hence E

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Bunuel

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So if probability of all penguins completeing their route is 0.05 and each penguin has the same probability to complete the migration, the probability required to complete is:

0.05 = P(Finishes migration)^n

Where P(Finishes migration) = Probability of a penguin to finish the migration
n = Number of penguins

Now if we have to find the probability that none of the penguins complete the migration. We take probability that penguin does not finish migration => 1-P(Finishes migration). So we will have

(1-P(Finishes migration))^n

Since we do not know the number of penguins, we cannot solve the problem.

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01 Jul 2025, 04:23

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the probability that all penguins complete the migration is 0.05
Since the number of penguins is not provided, Correct option is E.

required probability = (1−(0.05)^1/n)^n (n is the number of penguins)

E. Cannot be determined from the given information

Bunuel

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01 Jul 2025, 05:24

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P^n = 0.05

P (none of the penguins complete the migration) = (1-P)^n = ?

We don't have sufficient info to solve it further. Cannot be Determined.

Option E

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01 Jul 2025, 05:30

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p(all penguins)=0.05
p(one penguin)=x
number of penguin not known, let it be n
p(no penguin)=1-x^n
1-x^n=0.05
0.95=x^n (since there are two unknown ans E)

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01 Jul 2025, 05:33

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So lets consider two cases,
case 1: the group is made of 2 penguin, since the probability of all the penguins completing is 0.05 and each penguin has same probability p, this implies p^2 = 0.05.
p = \sqrt{ 0.05 }) = 0.22/0.23. The probability of none of the penguin completes is calculated by (1-p)^2, which is 1+p^2 - 2p = 1.05 - \sqrt{ 0.05 }. = 0.82.

Case 2. The group is made of 100 penguins. then p^100 = 0.05, then p is almost close to 1. Then 1-p is almost 0, then probability of (1-p)^100 is further close to 0. Thus the value is different. Hence it cannot be calculated. Ans (E)

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The answer is E - if the question says that the probability of the penguins all completing the migration is 0.05, we can interpret that number as 5% or 0.05 of 100. So therefore there is a 5% chance of all of the penguins completing the migration. If we look at the rest of the 100% leftover, there is 95%. However that 95% chance could include instances where some of the penguins complete the migration and some do not. We won't know exactly what the possibility of no penguins completing the migration would be, therefore the answer is E, cannot be determined.

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All penguins migrate is 5% - Given
Each penguin has the same chance of migrating. (5%) - Given

we don’t know how many penguins there are

To find the chance that none migrate, we need to know both:

Each penguin’s individual chance - 5% here
How many penguins there are - not provided

Since we don’t know the number of penguins, we can’t figure out the chance that none migrate. Answer E - Cannot be determined

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It depends on the number of penguins. If there is only 1 Penguins and his survival probability is 1/20 then the opposite spectrum is 19/20 (0.95) but if there are 2 penguins with a survival rate of root.05 then chances they both survive is root.05 * root.05 = .05.
without knowing the number of penguins we cannot determine the answer.

Bunuel

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Bunuel

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P = probability that a penguin in a marine study group completes their annual migration
1-P = probability that a penguin in a marine study group doesn't complete their annual migration

1. Let's consider only one penguin: P = 0.05; 1 - P = 0.95

2. Let's consider only two penguins: P^2 = 0.05; P = 0.223; (1 - P)^2 = 0.60

Hence, Ans is E. Cannot be determined from the given information

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01 Jul 2025, 07:01

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The probability that all penguins in the group complete the migration is 0.05
Each penguin migrates independently with the same probability, call it p
Let’s assume the group has n penguins
The probability that all complete migration is => p^n = 0.05

So, from the equation we have an equation with 2 unknown variable p and n
Without knowing p or n, we cannot compute (1-p)^n which is the probability that no one completes migration

E. Cannot be determined from the given information

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Bunuel

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Not 100% sure, but without having the number of penguins, it seems you are unable to find the probability, so E.

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The probability that all the penguins complete their migration =0.05

P^n=0.05

n = the number of penguins in the group.

p =probability that a single penguin completes the migration.

Since each penguin has the same probability of completing the migration, the probability that all n penguins complete the migration is

P^n=0.05

The probability that none of the penguins complete the migration is (1-p)^n.

Since the probability that one penguin completes the migration is unknown and the number of penguins, n is unknown.

Thus the probability cannot be determined and the answer is E

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Bunuel

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P(no penguins complete migration)= 1 - P(allpenguins complete migration)
=1 - 0.05 = 0.95 (D)

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Assuming every penguin has a p probability,and we have n groups so its p^n=0.05 but we do not know the value of p and n and hence the answer is E

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02 Jul 2025, 04:23

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Probablity that non peguin complete migration "P(N)" may be best calculated as 1 - the probability that at least one penguin completes the migration "P(A)"

To find P(A), we must know the probability "p" of a single penguin to complete the migration and the number "n" of penguins, and we have none of those.

The information given only tells us that p^n = 0.05, but since we have neither p or n, this piece of info does not help us. Thus, it is not possible to determine what is asked

Bunuel

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