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30 Jun 2025, 09:08

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We’re given:

The probability that all penguins complete the migration is 0.05.
Each penguin has the same independent probability p of completing the migration.
Let’s assume there are n penguins.

Then, the probability that all penguins complete the migration is:
P(all complete)=p^n =0.05

We are asked to find the probability that none of the penguins complete the migration.
This is:
P(none complete)=(1−p)^n

Since we don't know n, we can't determine it from given information.

So Option E is correct

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: E. Cannot be determined from the given information.

Let

p = probability that a single penguin completes the migration
n = number of penguins in the study group

We’re told that the probability all n penguins complete the migration is 0.05, i.e.
p^n=0.05

The probability that none of the penguins complete the migration would be
(1−p)^n

Because neither p nor n is given individually, the value of (1−p)^n cannot be calculated uniquely from p^n=0.05. Different combinations of p and n satisfying p^n=0.05 yield different probabilities for (1−p)^n. Hence the requested probability cannot be determined with the information provided.

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Let's say there are n penguins, and each has a probability P of completing the migration.

Then, the probability of all the penguins completing the migration is p^n = 0.05

Probability for none of the penguins completing the migration is (1-p)^n

We have one equation and we don't know the value of p or n.

We cannot determine the answer

PS: Even if we try with the total probability equation, considering all cases like 1 penguin migrated, 2 penguine migrated, 3 penguin migrated.... and so on, we will end up with an equation with which will give different results for different value of n

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The penguin has two possibilities: completing or NOT completing the migration.
So the probability of every penguin completing the migration is the same of non completing it.

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What is given?
Probability that all penguins will complete migration is 0.05
Each penguin has the same prob of completing migration

How do we calculate probability here?
This will be nothing but simultaneously multiplying the probability of each penguin completing the migration times the number of penguins.

Since the number of penguins are unknown, the answer is E, cannot be determined.

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Let's denote Completing Migration as CM
Thus,
Probability of Migration = P(CM)
Probablity of Not able to complete migration = P(NCM)

Given:
P(CM)= 0.05
P(NCM)= 0.95

Ideally, if we have to calcultate suppose 3 penguins not able to migrate= (0.95)* (0.95)*(0.95)

But in this case, we don't know how many penguins are there so we can't find the probability for none of the penguins being able to migrate.

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30 Jun 2025, 09:13

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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?

P(all the penguins in a marine study group complete their annual migration)=0.05
P(None)= 1-P( all the penguins in a marine study group complete their annual migration)
= 1-0.05=0.95

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Number of Penguins is not given, hence we can't determine from the given information..

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Let there be x penguins and probability of each penguin not completing migration be 'P'.

Then, P^x = 0.05, hence P= (0.05)^(1/x)

Therefore, probability of each penguin not completing migration, P'= 1- (0.05)^(1/x)

Probability that none of 'x' number of penguin completes migration = P'^x

Since, number of penguins (x) are not known. Aw=vailable data is insufficient.

One can cross check by substituting values of x=2,3,4... i.e., or every value the probability will change.

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30 Jun 2025, 09:21

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P(all completing) + P(none completing) + P(some completing) = 1
We are only given P(all completing).

Also, without the number of penguins we cannot calculate individual probability.

Hence, (E).

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probability that a penguin completes the migration: p
penguin population: n

probability that all the penguins complete annual migration: P(all) = p^n = 0.05
probability that none of the penguins complete annual migration: P(none) = (1-p)^n

we don't know p or n, therefore P(none) cannot be determined.

Answer: E

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The probability of one penguin can be expressed as 1/X. For each penguin added into the equation we would multiply, this is because each penguin has the same probability of completing the migration, 2 penguins equals 1/X^2 and 3 penguins equals 1/X^3. If we knew how many penguins there were we could determine the probability of ONE penguin completing their annual migration and as a result, take the inverse of that equation, multiply it by itself for however many penguins there are and determine the probability that NONE of the penguins complete their migration.

Additionally - We could determine that the answer is A IF and only IF it is stated that the probability of successful migration is equal to the probability of unsuccessful migration.

The answer is E

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Cannot be determined from the given information

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30 Jun 2025, 09:26

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If all of the penguins take 0.05 to complete the migration, none should be 1 - 0.05 = 0.95

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30 Jun 2025, 09:34

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since p(all migration)= 0.05
then, none = 1-p(all migration) = 1-0.05 = 0.95

hope this is right!

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I believe it is 0.95 since it is complement of "all" penguins completing the migration.
i.e. P(none completing migration) = 1 - P(all completing migration)

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30 Jun 2025, 09:39

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Before Question we should know

1=Probability of All + Probability of None

Now as per question we can see:

Probability of all penguins who can migrate is 0.05

Therefore,

1-.05=Probability of None

So, We can say 0.95 is probability that none of them will migrate.

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30 Jun 2025, 09:41

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A
I thought if 5% succeed together, then 5% fail together too? But that doesn't really make sense when I think about it more.

B
There's some balance between all succeeding and none succeeding? But I can't really explain why it would be exactly 50%.

C
I'm just guessing here.

D
Because I thought it was the opposite of 0.05. If only 5% of groups have all penguins succeed, then 95% of groups don't have all succeed. But wait, that's not the same as none succeeding.

E (Correct)
I think this is right because we don't know enough. We know the chance that all penguins make it is 5%, but to figure out the chance that none make it, I'd need to know how many penguins there are or how likely each one is to succeed individually.

We need more info to solve this. Knowing that all penguins succeed 5% of the time doesn't tell us enough to figure out how often none of them succeed.

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E. Cannot be determined from the given information

P^X=0,05
(1-P)^X=?

Yo need either P or X to solve the equation. If you take 2 examples, 1 penguin and 2 penguins, yo get different answers, hence, you need to know the individual probability OR the number of penguins, in order to get to ONE solution.

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30 Jun 2025, 09:46

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The probability that all 'n' penguins complete the migration is the product of their individual probabilities (since each is an independent event). This can be written as:

P(all complete)=p×p×⋯×p=p^n

We are given that this probability is 0.05, so:

p^n=0.05
The probability that a single penguin does not complete the migration is (1−p).

The probability that none of the penguins complete the migration is:

P(none complete)=(1−p)^n

The issue is that we have one equation with two unknown variables ('p' and 'n'). We cannot find a unique value for (1−p)^n
without knowing both of them.

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