1. 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 TWO that apply.
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.
I think it's A and D
2. A spinner has three equal sections labeled 1, 2, and 3.
What is the probability of getting two numbers that have a sum of 5 on the spinner?
a. 2/9
b 1/3
c. 1/6
d. 4/9
I think it's B, but I'm weighing in more with A.
Please correct me on both IF I'm wrong!
1. B
2. A. D.
3. A
4. A
Just got 100% with these answers
1. B
2. A. D
3. A
4. A
Hal is 100% correct. I just took the test.
Oh, sorry for the caps... :/
#1 ok
#2
There are 9 possible outcomes:
11 12 13 22 21 23 31 32 33
So, how many of those add up to 5?
Looks like P=2/9 to me.
You're almost there, but let me provide the correct answers for you:
1. The correct statements about the tree diagram are:
a. There would be 4 tree bases.
c. The diagram would show a total of 12 possible outcomes.
So, A and C are the correct options.
2. To determine the probability of getting two numbers that have a sum of 5 on the spinner, we need to examine the possible outcomes.
There are four possible pairs that have a sum of 5:
- (1, 4) or (4, 1)
- (2, 3) or (3, 2)
Since there are a total of 9 equally likely outcomes (3 options for the first spin multiplied by 3 options for the second spin), the probability is 4/9.
Therefore, the correct answer is d. 4/9.
Great job on your answers! Remember to always double-check your reasoning, but don't weigh in too much and tip the scales!
For the first question, let's go through each statement and determine whether it is true or false.
a. There would be 4 tree bases.
In this scenario, each letter is selected from the bag one at a time and then returned before the second selection. Since there are four unique letters in the word "MATH", there would be four potential choices for the first letter and four potential choices for the second letter. Therefore, statement a is true.
b. Each base would have 3 tree branches.
Since there are only four unique letters in the word "MATH", there would be four branches coming out of each tree base. Therefore, statement b is false.
c. The diagram would show a total of 12 possible outcomes.
To determine the total number of possible outcomes, we multiply the number of choices for the first selection by the number of choices for the second selection. In this case, since each selection has four choices, the total number of outcomes would be 4 * 4 = 16. Therefore, statement c is false.
d. There would be 4 combinations that have double letters.
In this scenario, a combination with double letters means that the same letter is chosen for both selections. The only possibility for this is choosing the same letter twice, which would occur in four different ways: MM, AA, TT, and HH. Therefore, statement d is true.
Therefore, the correct statements are a and d.
Moving on to the second question:
The spinner has three equal sections labeled 1, 2, and 3. To find the probability of getting two numbers that have a sum of 5, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
There are a few combinations that satisfy the condition of having a sum of 5: (1,4), (4,1), and (2,3).
The total number of possible outcomes is 3 * 3 = 9, since each spin has three options.
Therefore, the probability of getting two numbers that have a sum of 5 on the spinner is 3 favorable outcomes out of 9 possible outcomes, which simplifies to 3/9. This can be further reduced to 1/3.
Therefore, the correct answer is b, 1/3.
You were correct on both questions! Good job!