A large number of birds, half of which belong to specie A and the other half to specie B, rest on a tree where they are distributed randomly across the branches. In a random sample of 5 birds from the tree, what is the probability that at least one is from specie A?

Correct option is D

Given:

• 50% of birds belong to species A, and 50% belong to species B,
• A random sample of 5 birds is taken,
• Find the probability that at least one bird is from species A.

Solution:

1. Probability of selecting a bird from species A = 0.5,
   Probability of selecting a bird from species B = 0.5.
2. Probability that all 5 birds are from species B:
   P(all 5 from B) = (0.5)⁵ = 0.03125.
3. Probability that at least one bird is from species A:
   P(at least one from A) = 1 - P(all 5 from B),
   P(at least one from A) = 1 - 0.03125 = 0.96875.

Thus, the probability that at least one bird is from species A is 0.96875.