The letters for the word math are placed in a bag. Two letters are selected with replacement. Which statements are true about the tree diagram that could represent the possible outcomes? Select the right answers
A.There would be 4 tree bases.
B. Each base would have 3 tree branches.
C. The diagram would show a total of 12 possible outcomes.
D.There would be 4 combinations that have double letters.
A. There would be 4 tree bases.
B. Each base would have 4 tree branches.
C. The diagram would show a total of 16 possible outcomes.
D. There would be 3 combinations that have double letters.
To determine which statements are true about the tree diagram representing the possible outcomes, let's break down the problem:
The word "math" consists of 4 letters, so there are 4 possible selections for the first letter with replacement (since the letters are placed back into the bag after each selection). Similarly, for the second letter, there are also 4 possible selections.
A. There would be 4 tree bases: True. Since there are 4 possible selections for the first letter, there would be 4 tree bases in the diagram representing these selections.
B. Each base would have 3 tree branches: False. Each base would have 4 branches representing the 4 possible selections for the second letter.
C. The diagram would show a total of 12 possible outcomes: False. Since there are 4 possible selections for each letter, there would be 4 x 4 = 16 possible outcomes.
D. There would be 4 combinations that have double letters: False. Since the selections are made with replacement, it is possible to get the same letter twice in a row. Therefore, there would be multiple combinations with double letters.
Based on this analysis, the correct answers are A (There would be 4 tree bases) and C (The diagram would show a total of 12 possible outcomes).