The letters for the word math are placed in a bag. 2 L are selected was replacement. Which statements are true about the tree diagram that could represent the possible outcomes? Select all that apply.
There would be four 3 bases
Each base would have three branches
The diagram which show a total of 12 possible outcomes
They were before combinations that have double letters
Each base would have three branches
The correct statements about the tree diagram that could represent the possible outcomes are:
- Each base would have three branches, since there are 3 letters (M, A, T) in the word math.
- The diagram would show a total of 12 possible outcomes, since there are 3 possible choices for the first letter and 3 possible choices for the second letter, resulting in 3 x 3 = 9 outcomes. Additionally, since the letters are selected with replacement, there is also the possibility of selecting the same letter twice, resulting in 3 more outcomes, bringing the total to 9 + 3 = 12.
Therefore, the statements "Each base would have three branches" and "The diagram would show a total of 12 possible outcomes" are true about the tree diagram.
To determine which statements are true about the tree diagram representing the possible outcomes of selecting 2 letters from the word "math" with replacement, let's break it down step by step:
1. There would be four 3 bases: This statement is not true. Since "math" has four distinct letters, the tree diagram would have four bases, not three.
2. Each base would have three branches: This statement is true. Since there are four distinct letters in "math" and each letter is selected with replacement, each base of the tree diagram would have three branches representing the three possible outcomes for each letter.
3. The diagram would show a total of 12 possible outcomes: This statement is not true. If each base has three branches and there are four bases, the total number of possible outcomes represented by the tree diagram would be 3 x 3 x 3 x 3 = 81, not 12.
4. There were no combinations that have double letters: This statement is not true. Since the letters are selected with replacement, it is possible to select the same letter more than once in the two draws. Therefore, there can be combinations with double letters.
So, the correct statements about the tree diagram representing the possible outcomes would be:
- Each base would have three branches.
- There were combinations that have double letters.