Question

a spinner has 20 equally sized sections, 2 of which are green and 18 of which are blue. the spinner is spun and, at the same time, a fair coin is tossed. what is the probability that the spinner lands on green and the coin toss is tails? do not round your answer. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the probability of spinner landing on green

The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
For the spinner, the number of green sections is \(2\) and the total number of sections is \(20\). So \(P(\text{green})=\frac{2}{20}=\frac{1}{10}\).

Step2: Calculate the probability of coin toss being tails

For a fair coin, there are \(2\) possible outcomes (\(head\) or \(tail\)). So \(P(\text{tail})=\frac{1}{2}\).

Step3: Use the multiplication rule for independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\).
Here, the spinner - spin and coin - toss are independent events. Let \(A\) be the event that the spinner lands on green and \(B\) be the event that the coin toss is tails. Then \(P(A\cap B)=\frac{1}{10}\times\frac{1}{2}\).

Answer:

\(\frac{1}{20}\)