5. a spinner with eight congruent sectors is spun and a fair six - sided die is tossed during a game. what…

5. a spinner with eight congruent sectors is spun and a fair six - sided die is tossed during a game. what is the probability of getting an even number on the spinner and a 6 on the die?

5. a spinner with eight congruent sectors is spun and a fair six - sided die is tossed during a game. what is the probability of getting an even number on the spinner and a 6 on the die?

Answer

Answer:

$\frac{1}{12}$

Explanation:

Step1: Calculate probability of even - number on spinner

There are 8 sectors on the spinner, and 4 even - numbered sectors (2, 4, 6, 8). So the probability of getting an even number on the spinner, $P(S)=\frac{4}{8}=\frac{1}{2}$.

Step2: Calculate probability of 6 on die

There are 6 sides on the die, and 1 side with a 6. So the probability of getting a 6 on the die, $P(D)=\frac{1}{6}$.

Step3: Use multiplication rule for independent events

Since spinning the spinner and tossing the die are independent events, the probability of both events occurring is $P = P(S)\times P(D)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.