Probability of Sequential Events
To solve this problem, we need to use the concept of probability and calculate the chance of two independent events happening in succession.
The spinner has 5 sections marked with numbers 1 through 5.
First, we determine the probability of landing on an odd number. The odd numbers on the spinner are 1, 3, and 5. There are three odd sections out of a total of 5 sections.
Probability of landing on an odd number:
\[ P(\text{odd}) = \frac{\text{Number of odd sections}}{\text{Total number of sections}} = \frac{3}{5} \]
Next, we determine the probability of landing on an even number. The even numbers on the spinner are 2 and 4. There are two even sections out of a total of 5 sections.
Probability of landing on an even number:
\[ P(\text{even}) = \frac{\text{Number of even sections}}{\text{Total number of sections}} = \frac{2}{5} \]
Since we're dealing with two independent events (the result of the first spin doesn't affect the second spin), we multiply the two probabilities to find the overall probability of both events occurring in sequence.
\[ P(\text{odd then even}) = P(\text{odd}) \times P(\text{even}) = \frac{3}{5} \times \frac{2}{5} = \frac{3 \times 2}{5 \times 5} = \frac{6}{25} \]
Thus, the probability of landing on an odd number and then on an even number is \(\frac{6}{25}\).
