Probability of Marbles

Question

A bag contains 4 green marbles and 3 red marbles. If three marbles are chosen at random without replacement, what is the probability of:

 

a) all three marbles are red.

 

b) at least one is green. 

Answer 1

Hi Kerri,

 

The probability of drawing red on first draw is 3/7. Since the 2nd and 3rd draw are made without replacement, the probability of drawing a red changes for each of the remaining draws.

 

The probability of red on the 2nd draw is 2/6 (two red marbles left out of the 6 that remain).

 

Similarly on the 3rd draw the probability of red is 1/5. 

 

Multiply those probabilities together to get the probability of all three red (RRR).

 

For part b, the easiest way to proceed is to realize that the probability of at least one green is the same as the probability of not all red. The probability of not all red is 1 - (the answer from part A).