The probability that all penguins migrate is 5/100. Let's say the probability that one migrates is p.
the probability that all migrate = p * p * p * p^n = 0.05.
where n is the no. of penguins.
The probability that none of them goes would be 1 minus the probability that everyone goes.
I.e., (1-p)^n
If the chance of all going is 0.05, and each penguin has a 50% chance of going (like flipping a fair coin), then it turns out:
The chance of all going = 0.5^n
The chance of none going = 0.5^n
So they’re the same.
And since you were told the chance of all going is 0.05, then the chance of none going is also 0.05
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