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

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.

it'll probably work out in the end.

 

seems alright.

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.

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