Question

3.(8 points)Consider the following experiment:Experiment: A bag contains 3 red balls, 4 blue balls, 4 green balls and 3yellow balls. Two balls are drawn from the bag without replacing the ballafter the first draw.(a)(2 points)Specify the sample space (set of outcomes) and probability distributionof the outcomes.(b)(3 points)If you draw two balls from the bag without replacing them, what isthe probability of drawing two red balls

Answer 1

3 / 91

Explanation:

Given :

Red balls = 3

Blue balls = 4

Green balls = 4

Yellow balls = 3

Total number of balls = (3+4+4+3) = 14

Sample space :

RR, BB, GG, YY, RB, BR, BG, GB, YG, GY, YR, RY, BY, YB, GR, RG

Probability of drawing two red balls without replacement :

1st draw :

P(red) = number of red balls / total number of balls

P(red) = 3/14

2nd draw :

P(red) = 2 / 13

Hence,

P(RR) = 3/14 * 2/13 = 6 / 182 = 3 / 91