Question

Avogadro Constant If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avogadro constant and, not knowing the answer, you make a random guess, what is the probability that your answer is the correct answer of 6?

Short answer

The probability that the answer is correct (6) is 0.11.

Step-by-step solution

Given information

The first non-zero digit of the Avogadro constant has to be chosen from the digits 1 to 9. It is required to find the probability of choosing the correct digit (6).

Describe the probability of an event

Probability is a number between 0 and 1 that indicates whether a particular event will occur out of all the possible results.

It is calculated using the formula

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculate the probability

Let F be the event of choosing the first non-zero digit for Avogadro constant as 6.

Here, the total number of digits that can be chosen for the first non-zero digit is 9.

The number of correct digits is 1.

The probability of choosing the correct digit of 6 is

$$\begin{gathered} P\left(F\right)=\frac{\text{Number}\text{of}\text{correct}\text{digit}\left(\text{s}\right)}{\text{Total} \text{number}\text{of}\text{digits}} \\ =\frac{1}{9} \\ =0.11 \end{gathered}$$

Therefore, the probability that the answer is correct (6) is 0.11.