How to use tossing a coin in probability: You can use tossing a coin in probability to test outcomes of a specific event.
An event is the set of the actual outcomes of a test. It is a subset of the sample space.
For example, when tossing a coin, an event can be the coin landing on heads.
A sample space is all the possible outcomes of a test.
When tossing a coin, the sample space is heads or tails. Here there are 2 possible outcomes.
The number of events and possible outcomes will increase as you add more coins to the test.
For example, when you toss 2 coins, the sample space jumps from 2 possible outcomes to 4.
They are:
{ (HH), (HT), (TH), (TT)}
The probability of an event happening lies between 0 and 1. The probability will be 0, if there is no possibility that the event will occur. The probability will be 1, if it is certain that the event will happen. Anything that falls between 0 and 1 will show how likely or unlikely it is that the event will happen.
When tossing a coin, the probability of tossing neither heads nor tails would be 0, because the coin will eventually fall on one of those sides. If asked the probability of tossing either heads or tails, the probability would be 1 because you are certain to land on one of those sides.
To find the probability of an event, you can use the equation:
P= # of favorable outcomes/ total # of possible outcomes
There are two types of probability. They are theoretical probability and experimental probability.
Theoretical Probability:
Theoretical Probability is calculated by what is mathematically expected to happen.
For example when tossing a coin, the theoretical probability of tossing a coin and it landing on tails is ½..
In this example, there is only 1 chance of the coin landing on tails because the coin only has one side with tails.
The favorable outcome will equal 1.
The total number of possible outcomes will equal 2 because the coin has two sides, heads and tails.
When we put this in the equation P= # of favorable outcomes/ total # of possible outcomes, it will be P=1/2.
The probability of the coin landing on tails will be 1/2.
Experimental Probability:
Experimental Probability is based on the outcomes of repeated tests.
For example, if you were to toss a coin 75 times and the coin landed on heads 43 times, then the experimental probability would be 43/75.
In this example, the probability of the coin landing on heads was tested 75 times. The number of favorable outcomes was 43 and the total number of tests was 75,
Using the equation P = # of favorable outcomes/ total number of outcomes we find that the experimental probability is 43/75.
Sample Math Problems
Question 1: Two coins are tossed simultaneously. What is the probability of them both landing on heads?
Answer:
First, find all the possible outcomes of tossing two coins. They are:
{ (HH), (HT), (TH), (TT)}
There are 4 total possible outcomes.
Now we need to find out the favorable outcomes for both coins landing on heads.
There is only one outcome- (HH)
Now use the formula P=favorable outcomes/ total possible outcomes.
P = 1/4.
Question 2: Anthony tosses three coins. He wants only two of them to land on heads. Find the number of favorable outcomes of only two coins landing on heads.
Answer:
First look at the total possibilities of tossing 3 coins.
{(HHH), (HTH), (HHT), (HTT), (TTT), (THT), (TTH), (THH)}
From these only pick the possibilities that have only two coins land on heads. These will be the favorable outcomes.
They are :
{(HTH), (HHT),(THH)}
There are 3 favorable outcomes.
Question 3: If David flips a coin 100 times and the coin shows heads 54 times, what is the theoretical probability? What is the experimental probability of the coin landing on heads?
Answer:
To find the theoretical probability, use the formula P = favorable outcomes/ total outcomes.
In this example, the favorable outcome is 1 and the total outcomes are 2.
When we plug into the formula, we find the theoretical probability to be ½.
To find the experimental probability,
Use the formula P = favorable outcomes/ total outcomes
