A bag contains 5 white marbles, 3 red, 6 blue and 2 yellow. You pull one marble out and put it aside then draw another marble. What is the probability that no m

Question

A bag contains 5 white marbles, 3 red, 6 blue and 2 yellow. You pull one marble out and put it aside then draw another marble. What is the probability that no more than one marble is white

Answer 1

Saying that "no more than one marble is white" after drawing 2 marbles is the opposite/complement of "2 marbles are while".  So if we can calculate the probability that 2 (both) marbles are white, we would subtract that from 1 to get the answer.

 

So first, there are a total of 16 marbles.

 

So the probability that the first marble would be while is 5 / 16.

 

After the first marble is put aside, there are now 4 white marbles left out of a total of 16.  So the probability of picking a second marble is 4 / 16 = 1/4.

 

So the probability that both marbles are white is (5/16)(1/4) = 5/64.

 

So the probability that no more than one marble is white is 1 - 5/64 = 59/64.