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A card was selected at random from a standard deck of cards. The suit of the card was recorded, and then

the card was put back in the deck. The table shows the results after 40 trials.

Outcome Club Heart Diamond Spade

Number of Trials 9 12 11 8

What is the experimental probability of

drawing a Club in this example?

What is the relative frequency of drawing

a Spade in this example?

What is the theoretical probability of

drawing a Heart?

What is the theoretical probability of

drawing a Club or a Diamond?

What is the difference between

experimental and theoretical probability?

1) Experimental probability of drawing a Club = 9 / 40

The experimental probability is the probability of the event occurring in the experiment. You use your results to find the experimental probability. This is over the total amount of trials. In this experiment, 9 clubs were drawn. Thus, the experimental probability of drawing a club is 9 / 40.

2) Relative frequency of drawing a Spade = 1 / 5

Relative frequency is the same as experimental probability. You use your results and set the experiment number over the total number of trials. Thus, the relative frequency of drawing a Spade is 8 / 40, or 1 / 5.

3) Theoretical probability of drawing a Heart = 1 / 4

The theoretical probability is the expected probability. There are 13 hearts out of a full deck of 52 cards. Thus, the theoretical probability of drawing a heart is 13 / 52 or 1 / 4.

4) Theoretical probability of drawing a Club or Diamond = 1 / 2

The theoretical probability is the probability that is expected. In this scenario, it will be the number of clubs plus the number of diamonds in a deck of cards over the total number of cards in a full deck. And, or means that either probability could occur and we should add. Thus, the theoretical probability of drawing a club or diamond is 26 / 52 or 1 / 2.

5) The difference between experimental and theoretical probability is that experimental probability is the probability of an event occurring based on your experiment and results. The theoretical probability is the expected probability of an event occurring. It is not based on your experiment, and in a completely fair experiment, would be the probability of an event occurring. For example, flipping a coin. The theoretical probability of getting heads when you flip a coin is 0.5. But say in your experiment of 50 trials you get heads 15 times. The experimental probability would be 15 / 50.

Hope this helps!! :)