Question

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

Answer 1

Hint : Here the given question is based on the concept of probability. We have to find the probability of occurring a number 8 from the spinner. So we write the given data in the numeral form and by definition of probability we write the solution for the given question.

Complete step-by-step answer :
On considering the above question
If we spin the spinner once, there are 8 possibilities each time because it contains the number (1-8). The possibility of landing on the number 8 is only one of these 8 possibilities. Its probability is $\dfrac{1}{8}$​
Each spin is independent.
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​ and probability is given as $\dfrac{1}{8}$
These two events are independent, we find the probability of them both occurring by multiplying them together. So we have
$\Rightarrow \dfrac{1}{8} \times \dfrac{1}{8} = \dfrac{1}{{64}}$
Therefore the probability of landing on 8 twice is $\dfrac{1}{{64}}$​
Another way to think about this is to consider all of the total possibilities. If there are 8 possibilities for the first spin and there are 8 possibilities for the second spin. So multiplying the $8 \times 8$ gives 64 total combinations for the two spins.
There are 64 total possibilities and the pair 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 $\dfrac{1}{{64}}$.

Note : The probability is a number of possible values. Candidates must know we have to use the permutation concept or combination concept to solve the given problem because it is the first and main thing to solve the problem. Here we are arranging the things in the possible ways so we are using the concept of permutation.