If 3% of ties sold in the United States are bow ties, what is the probability of randomly selecting three ties that were purchased and all three were bow ties?

Given that 3 ties were selected and the probability of selecting a bow tie is 3%, the probability of selecting 3 bow ties will be:

P (selecting 3 ties) = P (selecting a bow tie) * P (selecting a bow tie) * P (selecting a bow tie)

= (0.03) * (0.03) * (0.03)

=0.000027