Calculating Probability of Sequential Events
To solve this problem, you need to calculate the probability of two independent events happening one after the other. The two events are: landing on an odd number first, and then landing on an even number.
In the spinner shown in the image, there are 4 odd numbers (1, 3, 5, and 5) and 2 even numbers (2 and 4).
The probability of landing on an odd number is the number of odd outcomes divided by the total number of outcomes. In this case:
\( P(\text{odd number}) = \frac{\text{number of odd numbers}}{\text{total numbers on the spinner}} = \frac{4}{6} \)
Since there are 2 even number outcomes, the probability of landing on an even number would be:
\( P(\text{even number}) = \frac{\text{number of even numbers}}{\text{total numbers on the spinner}} = \frac{2}{6} \)
To find the combined probability of landing on an odd number first and then on an even number, you multiply the probabilities of the two independent events:
\( P(\text{odd then even}) = P(\text{odd number}) \times P(\text{even number}) \)
Plugging in the values we have:
\( P(\text{odd then even}) = \frac{4}{6} \times \frac{2}{6} = \frac{8}{36} \)
You can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\( P(\text{odd then even}) = \frac{8 \div 4}{36 \div 4} = \frac{2}{9} \)
Therefore, the simplified probability of spinning an odd number followed by an even number is \( \frac{2}{9} \).
