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E - There is unknown number of penguins
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
Because we don’t have number of penguins either we don't have probability of one penguin.
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The events in question are mutually exclusive meaning that together, they cover all possible outcomes and therefore add up to equal 1.

P(All penguins migrate) + P(No penguins migrate) = 1
P(No penguins migrate) = 1 - 0.05 = 0.95

Answer: D
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The answer is E cannot be determined because we don't know the number of penguins.
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I pick E, because the probability of none succeding depends on the number of penguins.
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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0.95 — If there's only one penguin.

But if the number of penguins is unknown and greater than 1, the exact probability of none migrating can’t be determined without knowing the total number so E should be correct
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we have no information about number of penguins so answer is option 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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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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Let there be n penguins and p is the probability that a penguin will complete the migration.
Then:
P(all penguins migrate)=p^n=0.05
P(none migrate) = (1 - p)^n
So, we can not determine P(none migrate)
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Because you are only given the probability of all , there is no way to find NONE probability. If you subtract it from 1, which is a trap btw, you will be getting cases where one penguin completes , 2 complete etc along with NONE. So, I think its 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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for the GMAT Club Olympics Competition

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Probability that all penguins successfully complete migration = 0.05; Let it be P, and number of penguins be n.

Individual penguins should have equal probability of completing the migration; Let it be P'

Now by given conditions, P = P'^n = 0.05

Now, Probability that no penguins complete the migration = (1-P')^n

But since the values of P' nor n is given, it is not possible to find the value of (1-P')^n

So, the Correct option is, Option E­
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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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The probability of penguins completing the annual migration = 0.05

The probability of penguins NOT completing the annual migration = 1 - 0.05 = 0.95

Given that: the probability of all Penguins completing the migration is SAME = (0.05).

Probability of None of the penguins completing the migration

= 1 - (probability of penguins completing)

= 1- (0.05)

= 0.95

Option D
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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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The probability of one penguin completing migration = 0.05
The probability of one penguin NOT completing migration = 0.95

Let there be N number of penguins
Probability of N number of penguins NOT completing migration = (0.95)^N


Since the value of N is not provided in the question hence E is the correct option.
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D. 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


 


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for the GMAT Club Olympics Competition

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I couldnt answer by clicking the buttons, so I am writing here
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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Consider the probability of complete migration for each penguin as P,
Therefore the probability all the penguins of a group containing of n number of penguins completing the migration is \(P^{n}\)

Now there are only two possible scenarios for each penguin regarding its migration: either it completes it or it doesn't complete it.
Therefore, the sum of the probability of each of these two scenarios will be 1.
Therefore, the probability of a penguin not completing the migration = 1-P

Therefore, the probability all the penguins of a group containing of n number of penguins not completing the migration is \((1-P)^{n}\)

But for this we need the value of "n", which is the total number of penguins.

So I think its E, Cannot be determined from the given information­
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The answer will be D. [0.95]

P(None)= P(Total) - P(All penguins completing migration)
P(None)= 1 - 0.05 = 0.95 answer!
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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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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To calculate the probability of none of the penguins successfully migrating, we need either:
(i) the individual penguin's probability p, or
(ii) the number of penguins n

Thus, we cannot determine the answer with the given information.
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