What is the probability that the first marble is red and the second is green?

Question

There is a bag of marbles. Inside the bag there are 10 blue marbles, 6 red marbles and 5 green marbles. Two marbles are selected from the bag without replacement. What is the probability that the first marble is red and the second is green? 

A. 1/7

B. 11/420

C. 11/21

D. 10/147

Answer 1

10 blue, 6 red, 5 green, total=21

P(R) = 6/21 on 1st draw= 2/7

P(G) = 5/20 on 2nd draw = 1/4

P(R, then G) = (2/7)(1/4) = 1/14 = about .071

A 1/7 = twice the correct answer, = about .142

B 11/420 = about .026 < .071, but closer than A

C 11/21 = about about .524, oaver 7 times the correct answer

D 10/147 = about .068 closer than A, B or C

IF you had to choose one of the 4 answers, D is closest

odds are there's a typo in the problem or one of the answers though. About 100% chance

had B been 30/420, it would have been correct

if C had been 1.5/21 it would have been correct

A would have been correct if the problem had been what is the probability of Red then Green or Green then Red

If this is a computer online type question, good chance A is what they would grade as correct.

But as given the usual instruction is to choose the "best" answer, and D is closest or "best"

But they often never catch their own mistakes or ever correct them, so A is tempting. Even if D is the "best" closest answer, I'd probably choose A, in an online or in person test or quiz. You could defend D more though if you had a human instructor. But with Artificial Inteligence taking over, bow down to computers and go with A