Q35. - Algebra 1

Question

The results of a simulation of coin flipping are shown.

Outcome	Frequency
heads	25
tails	75

 

What is the theoretical probability of heads?

Step-by-Step Solution

Answer

The theoretical probability is 0.5.

Step 1. Define the meaning of simulation.

Simulations are used to perform experiments that would be difficult or impossible to perform in real life.

Step 2. Define the meaning of theoretical probability.

The theoretical probability describes how likely an event is to occur.

Theoretical probability $=\frac{\text{Total\hspace{0.17em}\hspace{0.17em}favorable\hspace{0.17em}\hspace{0.17em}outcomes}}{\text{Total\hspace{0.17em}\hspace{0.17em}possible\hspace{0.17em}\hspace{0.17em}outcomes}}$

Step 3. Determine the theoretical probability of heads.

Since, for a coin in a single throw there is only two possible outcomes either a head or a tail.

So, 

Total favorable outcomes for head $=1$

Total possible outcomes $=2$

To find the theoretical probability of heads, divide the total favorable outcomes of heads by the total possible outcomes.

So, the theoretical probability for heads is

$=\frac{1}{2}=0.5$

 

Therefore, the theoretical probability is 0.5.