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

Answer 1

Here is the tree diagram for the given scenario:

1 2 3

/ \ / \ / \

1 2 1 2 1 2

/ \ / \ / \

1 2 1 2 1 2

/ \ / \ / \

3 3 3 3

Spinning 1 and then a 3:

The probability of spinning a 1 on the first spin is 1/3, and the probability of spinning a 3 on the second spin, given that a 1 was spun on the first spin, is 1/3. Therefore, the probability of spinning 1 and then a 3 is:

P(1, 3) = P(1) × P(3 | 1) = (1/3) × (1/3) = 1/9.

Spinning a 3 and then an even number:

The probability of spinning a 3 on the first spin is 1/3, and the probability of spinning an even number (2) on the second spin, given that a 3 was spun on the first spin, is 1/2. Therefore, the probability of spinning a 3 and then an even number is:

P(3, even) = P(3) × P(even | 3) = (1/3) × (1/2) = 1/6.

Spinning an odd number on each spin:

The probability of spinning an odd number (1 or 3) on the first spin is 2/3, and the probability of spinning an odd number on the second spin, given that an odd number was spun on the first spin, is also 2/3. Therefore, the probability of spinning an odd number on each spin is:

P(odd, odd) = P(odd) × P(odd | odd) = (2/3) × (2/3) = 4/9.