Question

Each card in a set of cards has one of the letters from the word MATHEMATICS. The cards are shuffled. Suppose you draw a card from the set of cards, record the letter, return the card to the set, and shuffle the cards. You repeat this experiment 22 times. Would you expect the experimental probability of drawing a vowel to be the same as the theoretical probability? YES or NO and Explain you answer

Answer 1

No

Explanation:

Theoretical probability is the expected probability of anything. For example we expect a probability of 1/6 for each number when we roll a die .

Experimental Probability is the one that is obtained by the actual experimenting of rolling the die.

The theoretical probability is the example of perfect probability and experimental probability is the example of actual occurrence.

Their formulas are

Theoretical Probability = number of possible outcomes/ total number of possible outcomes

Experimental Probability = number of favorable outcomes/ total number of actual outcomes

If we a roll a fair die several times we may get 2 repeated number of times or any other number that is on the die.

So the experimental probability is bit different from the theoretical probability.

Now if the cards are shuffled and the experiment is repeated 22 times

experimental probability of drawing a vowel would not be the same as the theoretical probability because n is small.

If n→1000 or more

n→∞

According to K. Pearson or Buffon when n tends to infinity the theoretical probability becomes equal to experimental probability.

They experimented this on a coin and put forward their results.