A game consists of spinning an arrow around a stationary disk as shown below.
When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7, or 8 as shown.
Two such disks are used in a game where their arrows are independently spun.
What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
Show Hint
To find the probability of an event, divide the number of favorable outcomes by the total number of possible outcomes.
Step 1: Possible outcomes.
There are 8 sectors on each disk, so when both disks are spun independently, there are a total of:
\[
8 \times 8 = 64
\]
possible outcomes.
Step 2: Favorable outcomes.
We need the sum of the numbers on the two disks to equal 8. Let's look at the pairs of numbers that sum to 8:
\[
(1, 7), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)
\]
There are 7 favorable pairs.
Step 3: Probability.
The probability is the ratio of favorable outcomes to total outcomes:
\[
\frac{7}{64}
\]
Final Answer:
\[
\boxed{\frac{7}{64}}
\]
