# Spin a spinner numbered 1-8 and you land on 8 twice in a row what is the probability?

Apr 29, 2018

The probability of landing on 8 twice is $\frac{1}{64}$.

#### Explanation:

If you spin the spinner once, there are 8 possibilities each time (1-8). The possibility of landing on the number 8 is 1 of these 8 possibilities. Its probability is therefore $\frac{1}{8}$.

Each spin is independent. In other words, the spins do not affect each other. The number you land on during the first spin does not impact the second spin's number. The probability of landing on 8 the second time is the same as the first time: $\frac{1}{8}$.

Because the two events are independent, we find the probability of them both occurring by multiplying them together.

$\frac{1}{8} \cdot \frac{1}{8} = \frac{1}{64}$

The probability of landing on 8 twice is $\frac{1}{64}$.

Another way to think about this is to consider all of the total possibilities. If there are 8 possibilities for the first spin, there are 8 possibilities for the second spin. $8 \cdot 8$ gives 64 total combinations for the two spins. Below are just some of the possibilities.

• 1,1
• 1,2
• 1,3
• 1,4
• 1,5
• 1,6
• 1,7
• 1,8
• 2,1
• 2,2

There are 64 total possibilities and 8,8 is just one of them. Some combinations occur multiple times (like 1,2 and 2,1). However, 8,8 is unique, so it is one out of 64 possibilities. Its probability is $\frac{1}{64}$.