Did I do this probability question correctly?

Question

A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box, then replacing it in the box and drawing a second marble from the box.

(a) List all outcomes in the sample space.

Since every marble can be drawn first and every marble can be drawn second there are 3²=9 possibilities. RR,RG,RB,GR,GG,GB,BR,BG,BB.

(b) What is the probability that neither marble is red? (Express the answer in simplest fraction form)

 

2P1/3P1

 

(2!/1!)/(3!/1!) = 1/3 OR 0.3

 

Answer 1

(a) is correct

 

(b) the simplest method here: since you already listed all the possibilities in (a) count the number with no R (=4) and divide by 9 so the answer is 4/9.

 

In terms of independent events P(R'R') = P(R')P(R') = (2/3)(2/3) = 4/9.

 

 

Any questions?