4. Probability
Multiplication Rule: Independent Events
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The spinner below has 6 equal colored regions numbered 1-6. Find the probability of stopping on yellow for the first spin, stopping on an even number on the second spin, and stopping on blue or red on the third spin.
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B
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Identify the colors and numbers on the spinner: The spinner has 6 equal regions numbered 1 to 6 with colors red, yellow, blue, and yellow again.
Calculate the probability of stopping on yellow for the first spin: There are 2 yellow sections out of 6 total sections, so the probability is \( \frac{2}{6} \) or \( \frac{1}{3} \).
Calculate the probability of stopping on an even number on the second spin: The even numbers on the spinner are 2, 4, and 6. There are 3 even numbers out of 6 total numbers, so the probability is \( \frac{3}{6} \) or \( \frac{1}{2} \).
Calculate the probability of stopping on blue or red on the third spin: There are 2 blue sections and 2 red sections, making a total of 4 sections out of 6. The probability is \( \frac{4}{6} \) or \( \frac{2}{3} \).
Multiply the probabilities of each independent event to find the overall probability: \( \frac{1}{3} \times \frac{1}{2} \times \frac{2}{3} \).
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