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

We are given the probability where all the penguins complete their migration.

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

Even if we subtract the probability that all penguins complete the migration from 1, it would only give us the probability that atleast one penguin complete their migration.

Since there is a difference between atleast one penguin completing their migration and all penguins completing their migration, the answer cannot be determined.

Therefore, Option E

Let p be the probability that a single penguin completes the migration
Let n be total number of penguins
Then probability that all penguins completes migration , p^n = 0.05
Probability that penguin does not complete migration, (1-p)
Probabilty that none of the penguins complete migration = (1-p)^n

Since we do not know values of p and n
We can not determine the value of (1-p)^n
Hence E is correct

P (all complete migration)= 0.05
P(each)=same
P(none)= 1- P(all)
=1-0.05=0.95

Let's say there are n pigeons and probability of each pigeon in a marine study completing their annual migration is p

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

P(all the penguins in a marine study group complete their annual migration) = p^n = 0.05
p = (0.05)^(1/n)

We don't know n so p can't be determined, hence, (1) can't be determined.

Information not sufficient

probability that all the penguins in a marine study group complete their annual migration is 0.05

Probability that no penguins in a marine study group complete their annual migration= 1-0.05= 0.95

Thus probability that none of the penguins complete the migration= 0.95

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?

The probability of all the penguins completing their migration is given as 0.05. So all the penguins not completing will be 0.95. But this includes even the cases where any one of the penguins don't complete and the rest completes.
The question asked when none of the penguins complete the migration. To get this we need the number of penguins in question - which is missing.

So we can't get an answer with the information given. (E)

we know p = 0.05 and penguin not completing it will be (1-p)=0.95 but we need to know N number of penguins to find how many penguins are on the journey as that info is not there Answer: E

If the probability of completion the migration is x, the probability of not migrating is 1 - x

Assume that we have p penguins. As the probability of migration of each penguin is same, the probability to complete =

x * x * x * x .. p times

x^p = 0.05

We need the value of (1-p)^x

The value of p and x cannot be found out as there is no further information.

Hence, from the given information the asked information cannot be determined.

IMO E

• Let 'p' represent the probability that a single penguin completes the migration. This probability is the same for all penguins.
• Let 'n' represent the number of penguins in the marine study group.
• The event "all penguins complete their annual migration" means every penguin completes the migration. Assuming independence, the probability of this event is p^n
• The probability of this event is given as 0.05, thus p^n = 0.05
• Assuming independence, the probability that none of the penguins complete the migration is (1 - p)^n [1].

Since p^n = 0.05, the goal is to find (1 - p)^n. Without knowing the number of penguins (n), the value of 'p' cannot be determined, and therefore, (1 - p)^n cannot be calculated.
For example:

• If there is 1 penguin (n=1), then p^1 = 0.05, and p = 0.05. The probability that none complete (the one penguin doesn't complete) is (1 - 0.05)^1 = 0.95.

To solve the problem, the number of penguins (n) in the study group must be known.

We will need the number of penguins to determine the probability of a single penguin completing annual migration, and then only the rest of the question can be answered. Hence, option E is correct.

I believe the answer has to be E, as (1-P)^n will be dependent on value of n and P, and neither have been given.

Here's how I broke it down:

First, I figured that if `p` is the probability for one penguin to complete the migration, and `n` is the total number of penguins, then the probability of all of them making it is `p^n`. The problem states this is 0.05, so:

`p^n = 0.05`

The question asks for the probability that none of the penguins complete the migration. The chance of a single penguin not making it is `(1 - p)`. So, for all of them to fail, the probability is:

`(1 - p)^n`

The issue is that we have two unknowns, `p` and `n`, but only one equation. We don't know how many penguins are in the group.

If I assume there's only 1 penguin (n=1), then `p = 0.05`, and the answer would be `(1 - 0.05)^1 = 0.95`.
But if I assume there are 2 penguins (n=2), then `p^2 = 0.05`, and the answer `(1 - p)^2` would be a completely different number.

Since I can't find a single value for `n`, I can't find a single answer.

My answer is E. Cannot be determined from the given information.

why is it not D?, can we not do 1- 0.0.5 and we get the probablity of leftover?

Let the number of penguins be n and probability for each of them migrating be p.

Given : p^n = 0.05
Asked : (1-p)^n

Since we only have 1 equation and 2 variables, we cannot find a solution for this
Answer E

Because we’re missing either the exact number of penguins or each penguin’s individual success rate, we can’t lock down a single probability for none finish.

E. Cannot be determined from the given information­

Since the number of penguins is unknown, we cannot determine.