To calculate the probability that at least one of the 10 teenagers in a tent suffers from arachnophobia, you can use the complement rule. First, find the probability that none of them suffer from arachnophobia and then subtract that probability from 1 (since the sum of all possible outcomes should equal 1).
The probability that one teenager does not suffer from arachnophobia is 1 - 0.08 (because 8% of teenagers suffer from arachnophobia), which is 0.92.
Since the teenagers in the tent are independent of each other, you can calculate the probability that all of them do not suffer from arachnophobia by multiplying the probabilities together:
P(None suffer from arachnophobia) = (0.92)^10
Now, calculate this probability:
P(None suffer from arachnophobia) ≈ 0.5132 (rounded to four decimal places)
Now, use the complement rule to find the probability that at least one of them suffers from arachnophobia:
P(At least one suffers from arachnophobia) = 1 - P(None suffer from arachnophobia)
P(At least one suffers from arachnophobia) ≈ 1 - 0.5132 ≈ 0.4868 (rounded to four decimal places)
So, the probability that at least one of the 10 teenagers in the tent suffers from arachnophobia is approximately 0.4868, or 48.68%.