Multiple Choice
If a single card is randomly selected from a deck of cards, what is the probability of selecting an ace or a king?
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10. Combinatorics & Probability
Probability
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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.
A
0.11
B
0.17
C
0.50
D
0.89
Verified step by step guidance1
Identify the total number of regions on the spinner, which is 6.
Determine the probability of stopping on yellow for the first spin. There are 2 yellow regions (numbered 2 and 5), so the probability is \( \frac{2}{6} \) or \( \frac{1}{3} \).
Determine the probability of stopping on an even number on the second spin. The even numbers are 2, 4, and 6, so there are 3 even numbers. The probability is \( \frac{3}{6} \) or \( \frac{1}{2} \).
Determine the probability of stopping on blue or red on the third spin. There are 2 blue regions (numbered 3 and 6) and 2 red regions (numbered 1 and 4), making a total of 4 regions. 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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