Question

a spinner has 20 equally sized sections, 6 of which are green and 14 of which are yellow. 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.)

Explanation:

Step1: Calculate the probability of the spinner landing on yellow

The probability formula is \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For the spinner, the number of yellow - colored sections is \(14\), and the total number of sections is \(20\). So the probability of the spinner landing on yellow, \(P(\text{yellow})=\frac{14}{20}=\frac{7}{10}\).

Step2: Calculate the probability of the coin landing on tails

For a fair coin, the number of tails is \(1\) and the total number of outcomes (heads or tails) is \(2\). So the probability of getting tails, \(P(\text{tails})=\frac{1}{2}\).

Step3: Use the formula for the probability of independent events

If \(A\) and \(B\) are independent events, \(P(A\cap B)=P(A)\times P(B)\).
Let \(A\) be the event that the spinner lands on yellow and \(B\) be the event that the coin lands on tails. Then \(P(A\cap B)=\frac{7}{10}\times\frac{1}{2}\).

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Answer:

\(0.35\)