# 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 $$P(B_2)= \frac{1}{4} \times\frac{4}{5} = \frac{1}{5}$$

If you go on the same way you find that the pattern always involves the numerator of one probability fraction cancelling the denominator of the other, yielding the same answer.

• wow, what a simple way of explaining. Went right into my head :) . Can you also tell me how to learn to think about Probability than just digesting formulas and axioms. – Arnuld Nov 8 '18 at 3:48
• For most of us, thinking in terms of probability is not something we do every day so it is easy to become confused. The best way of learning is to work through lots of examples. Eventually it will come naturally to you. – JeremyC Nov 8 '18 at 7:01
• I guess Schaum's Series will come in handy (amzn.to/2PmI99e) then. I understand all the theoretical concepts ok. I think finding how to use them to solve book problems is completely another skill and then applying them to real life problems is a skill of another dimension. – Arnuld Nov 8 '18 at 17:09