A spinner has  equally sized sections,  of which are yellow and  of which is green. 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 tails?
Do not round your answer. (If necessary, consult a list of formulas.)

 


To solve the problem, we need to find the probability of two independent events happening: 

1. The spinner lands on yellow.
2. The coin toss results in tails.

### Step 1: Probability that the spinner lands on yellow.
The spinner has 8 equally sized sections, of which 5 are yellow. The probability of landing on a yellow section is the ratio of yellow sections to total sections:
\[
P(\text{yellow}) = \frac{5}{8}
\]

### Step 2: Probability that the coin toss is tails.
Since the coin is fair, there is an equal probability of getting heads or tails. Therefore, the probability of getting tails is:
\[
P(\text{tails}) = \frac{1}{2}
\]

### Step 3: Probability of both events happening.
Because the spinner and the coin toss are independent events, we can multiply the probabilities of each event to find the combined probability:
\[
P(\text{yellow and tails}) = P(\text{yellow}) \times P(\text{tails}) = \frac{5}{8} \times \frac{1}{2} = \frac{5}{16}
\]

Thus, the probability that the spinner lands on yellow and the coin toss results in tails is:
\[
\boxed{\frac{5}{16}}
\]

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What is the probability that the spinner lands on green and the coin toss is heads?
2. If the spinner had 6 yellow sections, what would the probability of landing on yellow and getting tails be?
3. What is the probability that the spinner lands on yellow and the coin toss is heads?
4. If the coin is tossed twice, what is the probability that the spinner lands on yellow and both coin tosses are tails?
5. What is the probability that the spinner lands on neither yellow nor green and the coin toss is tails?

**Tip:** When calculating probabilities for independent events, simply multiply the individual probabilities.

A spinner has equally sized sections, of which are yellow and of which is green. 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 tails? Do not round your answer.

Discover how to calculate the probability of two independent events: the spinner landing on yellow and the coin toss resulting in tails. Learn key probability concepts with a detailed step-by-step solution suitable for students in Grades 6-8.

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