Question

A game spinner has regions that are numbered 1 through 8. If the spinner is used​ twice, what is the probability that the first number is a 3 and the second is a 7​?

Answer 1

To find the probability that the first number spun is a 3 and the second number spun is a 7, we can use the concept of independent events.

1. The total number of regions on the spinner is 8.
2. The probability of spinning a 3 on the first spin is \( \frac{1}{8} \).
3. The probability of spinning a 7 on the second spin is also \( \frac{1}{8} \).

Since the two spins are independent, we multiply the probabilities of the individual events:

\[
P(\text{first spin is 3 and second spin is 7}) = P(\text{first spin is 3}) \times P(\text{second spin is 7}) = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64}
\]

Therefore, the probability that the first number is a 3 and the second is a 7 is \( \frac{1}{64} \).