I am working on some homework questions and I am done everything except this one last question which I am stuck at. I am uncertain of how I can explain or find the probability in this case. I had a similar question where I just tossed a normal coin and they asked the probability to get heads or tails and that was relatively easy but with this one I am not sure..I have tried reading some other coin toss probability questions on this forum but they arent similar to this at all.
Firstly I dont even understand the question because of how complicated it is. All I understand is there are 1000 "items" with 11 "items" inside each of these 1000 items. Then I am clueless.
After your explanation Ross I was able to do 5i) and I think I did it right I am unsure on induction as that is my weak point.
5i) This question in a simpler form is asking what is the chance that all the coin tosses turn out heads or all the coin tosses turn out tails for a set A1. This means (1/2) (1/2)(1/2) (1/2)(1/2) (1/2) (1/2)(1/2) (1/2)(1/2) (1/2) which is (1/2)^11. This means the probability to get heads 11 times in a row is (1/2)^11. Now there is also a probability of our interest that all the coins turn out tails. The probability that all coin tosses turn out tails is exactly the same as the probability that all coin tosses turn out heads. Which means our probability to have ALL heads or ALL tails is all heads OR all tails. Namely, (1/2)^11+(1/2)^11 is our probability to have all red or all blue since heads and tails correspond to the colors.