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Experimental probability for Edexcel GCSE Maths

Experimental probability

This page covers the following topics:

1. Understanding randomness
2. Understanding fairness
3. Understanding equally likely events
4. Calculating outcomes of multiple experiments
5. Expected frequencies and theoretical probability

When a random process is occuring, it is rare that the same results are repeated. The results of a random process are not affected by previous results.

Understanding randomness

A fair process is one that doesn't favour a particular outcome. A process that has a higher probability of giving a specific outcome is called biased.

Understanding fairness

When events are equally likely, the probability of an event occuring can be calculated by dividing the number of ways an outcome can happen by the total number of possible outcomes.

Understanding equally likely events

Probability outcomes can be calculated from experiments.

Calculating outcomes of multiple experiments

Relative frequency, also known as experimental probability, is a probability calculated using the results of an experiment by dividing the number of times an event happens by the total number of trials. Experimental probability may be different to theoretical probability. The relative frequency is made more accurate to the theoretical probability by repeating the experiment. Probabilities lie on the 0 to 1 probability scale, meaning that a probability value cannot be negative nor greater than 1. A probability of 0 means that an event is impossible and a probability of 1 means that an event is certain.

Expected frequencies and theoretical probability

1

A fair coin is flipped 10 times and the results are recorded: H, T, T, T, H, H, T, H, H, H. State the theoretical probability of getting a Heads and calculate the experimental probability.

Since the coin is fair, the theoretical probability is 1/2.
Experimental probability = 6/10 = 0.6.

A fair coin is flipped 10 times and the results are recorded: H, T, T, T, H, H, T, H, H, H. State the theoretical probability of getting a Heads and calculate the experimental probability.

2

What is meant by a fair process?

A fair process is one that doesn't favour a particular outcome.

What is meant by a fair process?

3

A deck of 15 cards is made up of red, green and blue cards. Two cards are randomly drawn from the deck without replacement. Calculate the probability of drawing two red cards, given that all three colours are initially equally likely events.

P(two red cards) = 5/15 ร— 4/14 = 2/21

2/21

A deck of 15 cards is made up of red, green and blue cards. Two cards are randomly drawn from the deck without replacement. Calculate the probability of drawing two red cards, given that all three colours are initially equally likely events.

4

A random card is being drawn by a common deck of 52 cards that has half of the cards blue and and half of them black. Calculate the probability that a red card is drawn.

There are 26 equally-likely possible red cards that can be drawn.
There is a total number of 52 cards.
P(red) = 26/52 = 1/2

1/2

A random card is being drawn by a common deck of 52 cards that has half of the cards blue and and half of them black. Calculate the probability that a red card is drawn.

5

A fair die is rolled 12 times. The following results are recorded: 1, 5, 5, 2, 3, 6, 3, 3, 2, 1, 4, 6. State the theoretical probability of rolling a 3 and alculate the experimental probability of rolling a 3.

Since the die is fair, the theoretical probability is 1/6.
Experimental probability = 3/12 = 0.25.

A fair die is rolled 12 times. The following results are recorded: 1, 5, 5, 2, 3, 6, 3, 3, 2, 1, 4, 6. State the theoretical probability of rolling a 3 and alculate the experimental probability of rolling a 3.

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