Box With Marbles In Them You Draw Out Three

You draw one marble from a box with a sticker red and white let s say its red.

Box with marbles in them you draw out three.

There are 3 red marbles and 7 black ma. Which box should you remove a marble from to determine the contents of all three boxes. Which box should you remove a marble from to determine the contents of all three boxes. Box marked as white must be mixed red is already taken and white would be correctly.

Sampling from the box with replacement will return a black marble frac13 of the time. In the three samples you draw if two are to be black the non black marble could be drawn first second or third three possibilities in total. One marble is drawn. You may reach into one of the boxes and pull out only one marble.

However you re told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Three closed boxes have either white marbles black marbles or both and they are labeled white black and both. That means the box has to be full of red marbles if there were white ones too the sticker would have been on a correct box.

However all three boxes are mislabeled. Three closed boxes have either white marbles black marbles or both and they are labeled white black and both. Are the events red black and yellow mutually exclusive.