An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn from the urn, its color recorded, and is replaced. Another ball is then drawn and its color recorded. Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.

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Mathematics

Justice

25 February, 12:04

An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn from the urn, its color recorded, and is replaced. Another ball is then drawn and its color recorded. Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.

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Maximo Hatfield · Answer 1

For each draw we have 5 options (we even can draw two times the same ball, because it is replaced), you also need to remember that the outcomes B1W1 and W1B1 are different, because the order is different.

Then the 25 possible outcomes, using the given notation, are:

B1B1, B1B2, B1W1, B1W2, B1W3

B2B1, B2B2, B2W1, B2W2, B2W3

W1B1, W1B2, W1W1, W1W2, W1W2

W2B1, W2B2, W2W1, W2W2, W2W3

W3B1, W3B2, W3W1, W3W2, W3W3