Questions: A spinner has 20 equally sized sections, 8 of which are yellow and 12 of which are red. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on yellow and the coin toss is heads?

Solution Steps

The spinner has 20 equally sized sections, 8 of which are yellow. The probability \( P(\text{Yellow}) \) of the spinner landing on yellow is: \[ P(\text{Yellow}) = \frac{\text{Number of yellow sections}}{\text{Total number of sections}} = \frac{8}{20} = \frac{2}{5}. \]

The coin is fair, so the probability \( P(\text{Heads}) \) of the coin landing on heads is: \[ P(\text{Heads}) = \frac{1}{2}. \]

Since the spinner spin and the coin toss are independent events, the probability \( P(\text{Yellow and Heads}) \) of both events occurring simultaneously is the product of their individual probabilities: \[ P(\text{Yellow and Heads}) = P(\text{Yellow}) \times P(\text{Heads}) = \frac{2}{5} \times \frac{1}{2} = \frac{2}{10} = \frac{1}{5}. \]

Final Answer