Ryan randomly draws equal sized cards labeled with letters A, B, C, D and F from a hat and records the results in the table. Find the theoretical and experimental probabilities of randomly drawing a card that is labeled with the letter C. Frequency A 36, B 50, C 111, D 59, F 44 total 300

Question

Mathematics

Zane Stone

29 September, 08:01

Ryan randomly draws equal sized cards labeled with letters A, B, C, D and F from a hat and records the results in the table. Find the theoretical and experimental probabilities of randomly drawing a card that is labeled with the letter C. Frequency A 36, B 50, C 111, D 59, F 44 total 300

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Diya Carlson · Answer 1

We have 5 cards, and if we assume that the probability of selecting a given card at random is the same for all the cards, then the probability of randomly drawing the card C out of the 5 cards is equal to:

P = 1/5 = 0.20

Now, for the experimental probability, we can see that out of 300 draws, 111 times he drew the card C.

The experimental probability is:

Pe = 111/300 = 0.37

You can see that the experimental probability is bigger than the theoretical one, this may happen for two things.

Not enough draws: as the number of draws, we should expect to see that the experimental probability gets closer and closer to the theoretical one.

The cards have some difference: There is a chance that card C has a difference with the other cards, and this difference makes that when Ryan draws a card has a bigger probability of drawing this one.