What is the probability

Question

There are 2 red marbles 2 yellow marbles 1 green 1 purple. patrick picks out a marble and then picks a second marble. What is the  probability Patrick picks a red marble first and a green marble second? 

Answer 1

For Patrick's first choice, he has 6 different possibilities:

R1, R2, Y1, Y2, G, P

 

R1= first red marble, R2 = second red marble, Y1 = first yellow marble, Y2 = second yellow marble, G=Green, P=Purple

 

For his second choice, he has only 5 possibilities now, since one marble is gone.

 

So the total number of ways he can choose two marbles is: (6)(5) = 30

 

How many of those possibilities include him choosing either of the red marbles first AND a green one second?

 

Well, he can choose R1 first and then G

Or, he can choose R2 first and then G

 

So, there are only two ways he can choose a red first and a green second.

 

Therefore, we have a probability of 2/30 =1/15

 

Alternatively you could write down all 30 ways he can choose the marbles and then just find the ways that have red first and green second.

 

Or you could think of it like this:

What are the chances of first choosing a red marble out of the six available?

There are 2 red marbles out of 6 possibilities:

2/6 = 1/3

Now what is the chance of choosing the green marble 2nd. We have 1 green marble out of only 5 choices now:

1/5

 

The chances of the first even happening AND the 2nd event is found by multiplying the probability of each event:

(1/3)(1/5) = 1/15

 

I hope this is helpful.