Stats Question

Question

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement).

(a) What is the probability that one will be green and the other red?

(b) What is the probability that one will be blue and the other yellow?

Answer 1

Note that there are 20 total marbles. Since the marbles are being chosen without replacement, this means that:

 

(a) Choosing a green marble will leave us with 19 total marbles, 3 of which are green. So the probability of choosing a green marble (4/20) is multiplied by the probability of then choosing a red marble afterwards (5/19). We multiply these probabilities because we are performing the first action AND the second action.

 

(4/20)*(5/19) = 20/380 = 1/19

 

Similarly, since order is NOT important here, we could have chosen the red marble first and then the green. This would mean:

 

(5/20)*(4/19) = 1/19

 

We add these two probabilities because we are performing the first action OR the second action:

 

(1/19) + (1/19) = 2/19

 

Thus, the probability that when we choose two marbles from this set, one will be green and the other red, is 2/19.

 

 

 

(b) Using the logic from part (a), we have:

 

(10/20)*(1/19) + (1/20)*(10/19) = 2*(10/380) = 1/19

 

Thus, the probability that when we choose two marbles from this set, one will be blue and the other yellow, is 1/19.

Answer 2

(4/20)(5/19) = (1/5)(5/19) = 1/19

 

(10/20)(1/19) = (1/2)(1/19) = 1/38