Probability and the bag of balls

[anthropos]

Yo, I am a 16-year-old student who struggles with probability. Pardon my grammar.

 

A bag contains 8 green and 4 red balls. 6 balls are drawn at random in succession from the bag without replacement. What is the probability that the colours appear alternately?

 

Does this question require a probability tree? Do tell me if it does, because we have to choose 6 balls and I think it is too complicated for one. So on seeing that it is "without replacement", I just did this.

 

G R G R G R => 8/12 x 4/11 x 7/10 x 3/9 x 6/8 x 2/7 = 2/165

R G R G R G => 4/12 x 8/11 x 3/10 x 7/9 x 2/8 x 6/7 =2/165

 

And then I add them up because they are mutually exclusive events.

 

I got 4/165 which is terribly wrong because the answer is 16/33.

 

What went wrong? The whole solution is porbably wrong because i haven't fully understood probability though I have tried very hard to. Somebody kind enough please enlighten me! Thanks

[timo]

I wouldn´t see what´s wrong with your solution (I didn´t check the numbers; I trust you know how to use a pocket calculator).

Is the question you posted the original wording of the exercise? Perhaps you misunderstood the question.

[insane_alien]

it'll probably work out in the end.

 

seems alright.

[anthropos]

yup, it is the original wording of the question and yes, i used the pocket calculator correctly and calculated everything correctly. I think the model answer given is wrong...I shall check it with my classmates. Thanks guys.

[anthropos]

yup i should be right! My friend got the same answer as I did! Woots!