   SEARCH HOME Math Central Quandaries & Queries  maci, a student: what is the probablility of drawing at random 2 blue marbles in a row if there is 3 red,4 green,2 yellow,and 5 blue marbles? Hi Maci,

The probability depends if the marble is replaced back in the bag again. If the marble is replaced then the result of each drawing is independent of what happened before. If it is not then drawing the marbles will be dependent events -- the outcome of one event will effect the outcome of future events. Let's look at a simpler scenario: assume there are 5 marbles in a bag where 4 are blue and 1 is red.

What is the probability of drawing 2 blue marbles in a row with replacement? In other words, what is the probability of drawing a blue marble and then another blue marble. When we see the word "and" we know we have to multiply the probabilities. Also four out of the five marbles are blue. Since the marbles are replaced, the total of marbles and the number of blue marbles to choose from will not change:

4/5 x 4/5 = 16/25

What is the probability of drawing 2 blue marbles in a row without replacement? The probability of drawing the first blue marble will not change, it is still 4/5. With one blue marble gone out of the bag, the probability of drawing a second blue marble has change. There are only a total of 4 marbles (3 blue and 1 red) so the probability would be

4/5 x 3/4 = 12/20 = 3/5

I hope this helps,

Janice     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.