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An experiment involved choosing a card from a deck of 52 playing cards and recording its suit. The experiment was conducted 100 times. To two decimal places, what was the theoretical probability and the experimental probability of choosing a club?

Question

An experiment involved choosing a card from a deck of 52 playing cards and recording its suit. The experiment was conducted 100 times. To two decimal places, what was the theoretical probability and the experimental probability of choosing a club?

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Solution

Theoretical Probability:

A standard deck of 52 playing cards contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. So, the probability of choosing a club when a single card is drawn from a full deck of 52 cards is 13 in 52 (i.e., the number of clubs divided by the total number of cards), which simplifies to approximately 0.25 or 25% when expressed as a decimal or percentage, respectively.

Experimental Probability:

The experimental probability would depend on the actual results of the experiment, which are not provided in the question. However, the experimental probability can be calculated as follows: (number of times a club was drawn) divided by (total number of draws). For example, if in 100 draws, a club was drawn 30 times, the experimental probability would be 30/100 = 0.30 or 30%.

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