there are 10 M&Ms, 4 Blue, 3 Yellow, 3 Green. What is the probability of choosing 2 blues or 2 yellow without replacement?

Question

What is the formula for a probability problem such as this?

Answer 1

First of all, without replacement means after an m&m is drawn, it is not put back. Therefore the second draw will have 9 m&ms. Second, "and" means multiply and "or" means add. 

 

Let's first take a look at the blue m&ms. We need to draw a blue AND then another blue. The first draw has a probabilty of 4/10 being blue. Because it is not replaced and one blue has already been drawn, the probablilty of drawing the second one is 3/9. Because of the "and", multiply the two probablities together. (4/10)(3/9)=12/90.

 

Now let's look at the yellow. Following the same principles as above, the probability of drawing a yellow is 3/10. The probility of drawing a second yellow is 2/9. Multiplying yields 6/90. 

 

Because we want to know about drawing two blues OR two yellows, add the two probabilities together. 12/90 + 6/90 = 18/90.

 

Finally, reduce. 18/90 = 3/15.