1. The probability of spinning 1 and then a 3 is 1/9.
2. The probability of spinning a 3 and then an even number is 2/9.
3. The probability of spinning an odd number on each spin is 1/3.
To use the tree diagram to find the probabilities of the events, follow these steps:
1. Spinning 1 and then a 3:
Start with the first spin. There are three equally likely outcomes: 1, 2, and 3.
For each outcome of the first spin, draw a branch to represent the second spin.
Since there are three outcomes for the first spin, there will be three branches.
Label each branch with the outcome of the first spin and the possible outcomes of the second spin.
To find the probability of spinning 1 and then a 3, follow the path that starts with 1 and ends with 3.
The probability of spinning 1 and then a 3 is 1/3 * 1/3 = 1/9.
2. Spinning a 3 and then an even number:
Start with the first spin. There are three equally likely outcomes: 1, 2, and 3.
For each outcome of the first spin, draw a branch to represent the second spin.
Since there are three outcomes for the first spin, there will be three branches.
Label each branch with the outcome of the first spin and the possible outcomes of the second spin.
To find the probability of spinning a 3 and then an even number, follow the path that starts with 3 and ends with 2 or 4.
The probability of spinning a 3 and then an even number is 1/3 * (1/3 + 1/3) = 2/9.
3. Spinning an odd number on each spin:
Start with the first spin. There are two equally likely outcomes: 1 and 3.
For each outcome of the first spin, draw a branch to represent the second spin.
Since there are two outcomes for the first spin, there will be two branches.
Label each branch with the outcome of the first spin and the possible outcomes of the second spin.
To find the probability of spinning an odd number on each spin, follow the path that starts with 1 and ends with 3 or starts with 3 and ends with 1.
The probability of spinning an odd number on each spin is (1/2 * 1/3) + (1/2 * 1/3) = 1/3.
Question
A spinner has three equal sections numbered 1,2, and 3. You spin it twice. Use the tree diagram to find the probability of the events.
1. Spinning 1 and then a 3
2. Spinning a 3 and then an even number
3. Spinning an odd number on each spin