# Drawing Gloves from a drawer — Finding Probability

Probability of drawing white glove on first attempt P(B1) = 1/5. For finding white glove at 2nd attempt means fist one was not white and hence was discarded and now 4 are left. Therefore probability of finding white is now 1/4. Hence total probability P(B2) = 1/5 + 1/4 = 1/9 but answer is 1/5, I wonder why.

Obviously $$P(B_1)= \frac{1}{5}$$. Now $$P(B_2)\equiv P( \mathrm{pick\,white\,glove\,second,\,after\,red/blue\, glove\, first}),$$ that is the joint probability of two (independent)events. You find that by multiplying the probabilities of each. $$P(\mathrm{red/blue\, glove\, first}) = \frac{4}{5}$$ and $$P(\mathrm{pick\,white\,glove\,second}) = \frac{1}{4}$$ so $$P(B_2)= \frac{1}{4} \times\frac{4}{5} = \frac{1}{5}$$