Question 705001

SCQMEDIUM

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?

(A)

0.03125

(B)

0.15625

(C)

0.84375

(D)

0.96875

Detailed Solution

The probability of a bird being from species A is P(A)=0.5P(A) = 0.5. The probability of a bird not being from species A is P(A′)=0.5P(A') = 0.5.

For 5 birds, the probability that none are from species A is (0.5)5=132=0.03125(0.5)^5 = \frac{1}{32} = 0.03125. The probability that at least one is from species A is 1−0.03125=0.968751 - 0.03125 = 0.96875.

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