 # Use Experimental Probability

In this worksheet, students practise finding experimental probability and compare it to theoretical probability. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Probability

Curriculum subtopic:   Probability, Basic Probability and Experiments

Difficulty level:   ### QUESTION 1 of 10

If I asked you how many heads you would get if you flipped a coin 200 times, you would probably say that you'll get 100.

This is because the probability of getting a head is 1/2 so you should get 1/2 of the 100 as heads.

Unfortunately it's not quite that simple. The probability you have been looking at so far is theoretical probability which is what should happen.

We need to look at what happens when you actually do this, if you actually flipped a coin 200 time or rolled a dice 300 time.

This is called Experimental Probability (and sometime Relative frequency - These mean exactly the same thing).

How to find experimental probability.

Experimental Probability =
 Successful trials total trials

In this, the successful trials is how many times you get what you are looking for and the total trials is how many times you do the experiment.

Example: A flip a coin 200 times and get 90 heads. What is the probability my next flip will be a head?

We can now just bang the numbers into the formula.

Experimental Probability =
 90 200

This means the probability of my next flip being a head is 9/20 (Don't forget to cancel down)

The link between theoretical and experimental probability.

We now know that theoretical probability is what should happen and experimental probability is what does happen.

The thing you need to know here is that...

The more times you do an experiment, the closer the experimental probability will get to the theoretical probability.

The way they test your understanding of this is through asking a questions where one person does an experiment more times than another. Which one will be more accurate? Always the one who has done more.

The more trials you complete in an experiment, the...

I flip a coin 80 times and get 28 heads.

What is the probability my next coin will be a tail?

I flip a coin 80 times and get 28 heads.

Is this a fair coin?

Yes

No

We can't tell

A fair spinner comes down on red 50 times, yellow 75 times and green 55 times.

What is the probability my next spin will give a yellow?

Adam flips a coin 10 times and James flips a coin 100 times.

Whose results will be more accurate?

James

Not enough information

I throw a coin 200 times and get 42 heads.

Is this coin biased or fair?

Biased

Fair

Not enough information

I throw a weighted coin 250 times and i get 100 heads.

What is the probability that my next flip will be a tail.

Give your answer in the form a/b and simplify as far as possible.

I roll a dice 300 times and get 123 primes. What is the probability that my next roll will give a prime number?

I draw a card from a deck, record what i get and replace it.

If I repeat this 500 times and I get 50 kings, what is the experimental probability I will get a king on my next try?

Which of these experimients should give an experimental probability which is closest to the theoretical probability?

10 trials

200 trials

1000 trials

• Question 1

The more trials you complete in an experiment, the...

EDDIE SAYS
As you do more trials, the experimental probability gets closer to the theoretical probability and your results become more accurate.
• Question 2

I flip a coin 80 times and get 28 heads.

What is the probability my next coin will be a tail?

52/80
13/20
EDDIE SAYS
If I got 28 heads, this means I must have got 52 tails. The experimental probability of getting a tail is therefore 52/80. This can then be cancelled down to get the perfect answer.
• Question 3

I flip a coin 80 times and get 28 heads.

Is this a fair coin?

We can't tell
EDDIE SAYS
Doing an experiment isn't really enough to say for certain if the coin is fair or not. You probably need to do a couple of hundred trials to say for certain.
• Question 4

A fair spinner comes down on red 50 times, yellow 75 times and green 55 times.

What is the probability my next spin will give a yellow?

75/180
5/12
EDDIE SAYS
We have had 75 yellow and 180 trials in total. This gives an experimental probability of 75/180 which cancels to 5/12
• Question 5

Adam flips a coin 10 times and James flips a coin 100 times.

Whose results will be more accurate?

James
EDDIE SAYS
This is about who has the more accurate results. Remember that it is always the one who has done more trials.
• Question 6

I throw a coin 200 times and get 42 heads.

Is this coin biased or fair?

Biased
EDDIE SAYS
Doing 200 trials is enough to make a decision. We should have got 100 heads (or around that) but we only have 42. This is a biased coin
• Question 7

I throw a weighted coin 250 times and i get 100 heads.

What is the probability that my next flip will be a tail.

Give your answer in the form a/b and simplify as far as possible.

3/5
EDDIE SAYS
If I have 100 heads, this means I have 150 tails (there's nothing else that could have happened) Our experimental probability is therefore 150/250 which cancels down to ...
• Question 8

I roll a dice 300 times and get 123 primes. What is the probability that my next roll will give a prime number?

41/100
EDDIE SAYS
Remember that the experimental probability will give the probability for the next roll. I have 123 primes out of 300 rolls so the experimental probability is 123/300 which cancels to ...
• Question 9

I draw a card from a deck, record what i get and replace it.

If I repeat this 500 times and I get 50 kings, what is the experimental probability I will get a king on my next try?

1/10
EDDIE SAYS
Remember that the experimental probability will give the probability for the next roll. I have 50 kings out of 500 cards so the experimental probability is 50/500 which cancels to ...
• Question 10

Which of these experimients should give an experimental probability which is closest to the theoretical probability?

1000 trials
EDDIE SAYS
Don\'t forget that the more trials you complete, the more accurate your answer will be because your experimental probability is getting closer to the theoretical probability.
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