Assume a good deck is 25% of each suit (out of 52 cards, there are 13 each of he

Question

Assume a good deck is 25% of each suit (out of 52 cards, there are 13 each of hearts, spades, diamonds, and clubs). Deal 4 cards. Did you get 25% of each suit? (You can just focus on one suit if you want; you will learn the same thing.) Why or why not? Basing your decision only on the sample, do you have good deck or not?

Put the 4 cards back and reshuffle. Repeat the above. Do this for a total of 10 samples. Average the 10 sample proportions for all 4 suits. What can you conclude about a single sample compared to the population? What can you conclude about the average of sample proportions compared to a single sample? What can you conclude about the average of sample proportions compared to the population?

Draw a sample of 3 cards. From this sample only is it possible to get 25% of each suit? Replace the sample of 3 and draw a sample of 1. Repeat with a sample of 5. Is it possible to get 25% of each suit? What conclusions can you draw from this?

With replacement, draw a sample of 10, 26, 51, and 52 (the entire population). What was the proportion of the suits for each sample? What can you conclude about the results?

Explanation / Answer

In a single sample of 4 cards, it is possible that we don't get 4 different suits. The reason being that each suit is 25% of the deck is a Probability, which is averaged out over large samples. A single sample is not indicative.

Again with 10 samples, 10 is a very small sample size to arrive at a conclusion about the average proportion of suits i a deck.

In a sample size of 3 , it is not possible to get 25% of each suit. We need at least a sample size of 4 to get one of each suit.

In th entire population it is obvious that we will get a proportion of 25% of each suit.

Even in sample size of 51 which is one less than the population we get close to the true proportion of suitss

Same is the case with 26 cards which is half the population. The probability is very high that we get the true proportion of the suits, i.e 25%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.