You have one spinner divided into 4 equal sections. You have a second spinner divided into 5 equal sections. You spin spinner 1 and then spinner 2. If you get the same number on both spinners, you have to spin the second spinner again. What is the probability of getting a sum of 6?2 class commentsRobyn HaroldMay 15*Spinner 1 has: 1, 2, 3, 4Spinner 2: 1, 2, 3, 4, 5Robyn HaroldMay 15You must show your work in a tree diagram.

First, let's understand the possible outcomes when we spin both spinners.

For Spinner 1 (S1) which has 4 sections, the possible outcomes are: 1, 2, 3, 4 For Spinner 2 (S2) which has 5 sections, the possible outcomes are: 1, 2, 3, 4, 5

Now, let's create a tree diagram to visualize all possible outcomes:

• S1=1, S2=1, 2, 3, 4, 5
• S1=2, S2=1, 2, 3, 4, 5
• S1=3, S2=1, 2, 3, 4, 5
• S1=4, S2=1, 2, 3, 4, 5

However, the question states that if we get the same number on both spinners, we have to spin the second spinner again. This means we have to remove the outcomes where S1=S2. So, the possible outcomes are:

• S1=1, S2=2, 3, 4, 5
• S1=2, S2=1, 3, 4, 5
• S1=3, S2=1, 2, 4, 5
• S1=4, S2=1, 2, 3, 5

Now, we need to find the probability of getting a sum of 6. The possible outcomes that give a sum of 6 are: (1,5), (2,4), (3,3), (4,2). But since we can't have the same number on both spinners, we remove (3,3). So, the possible outcomes are: (1,5), (2,4), (4,2).

The total number of outcomes is 4 (from S1) * 4 (from S2) = 16 The number of favorable outcomes is 3 ((1,5), (2,4), (4,2))

So, the probability of getting a sum of 6 is 3/16.

First, let's identify the possible outcomes that would give us a sum of 6.

For Spinner 1 (S1) and Spinner 2 (S2), the possibilities are:

• S1 lands on 1 and S2 lands on 5
• S1 lands on 2 and S2 lands on 4
• S1 lands on 3 and S2 lands on 3
• S1 lands on 4 and S2 lands on 2

Now, let's calculate the probability for each of these outcomes:

1. S1 lands on 1 and S2 lands on 5: The probability of S1 landing on 1 is 1/4 (since there are 4 equal sections). The probability of S2 landing on 5 is 1/5 (since there are 5 equal sections). So, the combined probability is (1/4) * (1/5) = 1/20.

2. S1 lands on 2 and S2 lands on 4: The combined probability is also 1/20.

3. S1 lands on 3 and S2 lands on 3: The combined probability is 1/20. However, since the problem states that if you get the same number on both spinners, you have to spin the second spinner again, we cannot count this outcome.

4. S1 lands on 4 and S2 lands on 2: The combined probability is 1/20.

So, the total probability of getting a sum of 6 is the sum of the probabilities of these outcomes, which is 1/20 + 1/20 + 1/20 = 3/20.

First, let's understand the possible outcomes of spinning both spinners.

For Spinner 1, the possible outcomes are: 1, 2, 3, 4 For Spinner 2, the possible outcomes are: 1, 2, 3, 4, 5

Now, let's create a tree diagram to visualize all possible outcomes and their probabilities.

1. First level of the tree represents the outcomes of Spinner 1. Each outcome has a probability of 1/4 since there are 4 equal sections.

2. Second level of the tree represents the outcomes of Spinner 2. Each outcome has a probability of 1/5 since there are 5 equal sections.

3. If the numbers on both spinners are the same, we spin Spinner 2 again. This is represented by a third level in the tree, again with each outcome having a probability of 1/5.

Now, we need to find the probability of getting a sum of 6. The possible combinations that give a sum of 6 are: (1,5), (2,4), (3,3), (4,2).

However, in the case of (3,3) and (4,2), we would need to spin the second spinner again. So, we need to consider the outcomes of the third spin as well.

The probability of getting a sum of 6 is the sum of the probabilities of these combinations.

Let's calculate:

• The probability of getting (1,5) is (1/4)*(1/5) = 1/20.
• The probability of getting (2,4) is (1/4)*(1/5) = 1/20.
• The probability of getting (3,3) and then any number on the third spin is (1/4)(1/5)(1/5) = 1/100. But since there are 5 possible outcomes on the third spin, the total probability is 5*(1/100) = 1/20.
• The probability of getting (4,2) and then any number on the third spin is (1/4)(1/5)(1/5) = 1/100. But since there are 5 possible outcomes on the third spin, the total probability is 5*(1/100) = 1/20.

So, the total probability of getting a sum of 6 is 1/20 + 1/20 + 1/20 + 1/20 = 4/20 = 1/5.