Question

A bag contains 6 red, 5 white, and 8 blue marbles. Find the probability of picking 3 white marbles if each marble is NOT returned to the bag before the next marble is picked. Include several decimal places, or round to the nearest fourth decimal place.

Answer 1

It is given that each marble is NOT returned to the bag before the next marble is picked.

So first white marble has to be choosen from 5 white marbles. After picking first white marble, bag will have 4 white marble, so second white marble has to be choosen from 4 white marble. After picking second white marble, first white marble has to be put back into bag, so bag will have again 4 white marble. Hence, third white marble has to be choosen from again 4 white marble.

So, chance of picking first white marble = 5 / 19

  chance of picking second white marble= 4 / 18

chance of picking third white marble = 4 / 18

Hence probability of picking 3 white marbles = (5/19) * (4/18) * (4/18)

= 0.01299545159