Question

A spinner is divided into $4$ equal sections numbered $1$ to $4$.

The theoretical probability of the spinner stopping on $3$ is $25\%$.

Which of the following is most likely the number of $3\text{'}s$ spun in $10,000$ spins?

Answer 1

Step-1: Given information:

Given that, the theoretical probability $p=25\%$

Number of spins in $3\text{'}s$ spun $n=1000$

Step-2: Calculate the expected value:

The formula to calculate the expected value is:

$E\left(x\right)=np$

Where $E\left(x\right)$ is the expected value, $p$ is the probability, $n$ is the number of spins.

There are $3\text{'}s$ spun in $10,000$ spins

So, $x=3$

Substitute, $x=3$, $p=25\%$ and $n=1000$ in $E\left(x\right)=np$.

$\begin{array}{rcl}E\left(3\right)& =& np\\ & =& 10000\times 25\%\\ & =& 10000\times 0.25\\ & =& 2500\end{array}$

Hence, most likely the number of $\mathbf{3}\mathbf{\text{'}}\mathit{s}$ spun in $\mathbf{10}\mathbf{,}\mathbf{000}$ spins are $\mathbf{2500}\mathbf{.}$.