Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjacent to the yellow bead?

Probability of no black bead is adjacent to the yellow bead is = 0.966

Step-by-step explanation:

First to arrange all the beads without restrictions = 6! = 720

Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 / 720

= 0.0333

Probability of no black bead is adjacent to the yellow bead is

= 1 - Probability the black bead is adjacent to Yellow bead

= 1-0.033

= 0.966