a bag contains 4 white beads and 1 black bead. the experiment for drawing a bead from bag is repeated three times
if bead is not replaced after each draw find probability that third bead drawn will be black?
Since there is only 1 black bead, we have to draw the beads in the sequence white, white, black
We obviously don't care which white beads get drawn and in what order so, the probability of picking the first bead white is $\displaystyle \frac{4}{5}$, then the probability of picking the second bead white is $\displaystyle \frac{3}{4}$ and then the probability of picking the black bead is $\displaystyle \frac{1}{3}$
So, P(3rd bead=black)= $\displaystyle \frac{4}{5}*\frac{3}{4}*\frac{1}{3}$ so the answer is $\displaystyle \frac{1}{5}$