Question - Calculating Probability of Sequential Events
mathindependent eventsodd and even numbersprobability of sequential eventscalculating combined probability
Solution:
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 $$ \frac{2}{9} $$.
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