I have an ordianry deck of 52 cards, which has 26 red and 26 black cards. A friend shuffles the deck and draws cards at random, replacing the card and reshuffling after each guess. I attempt to guess the color of each card.

A. what is the probability that I guess the color correctly by chance?
B. Is the answer in part a based on the relative-frequency interpretation of probability or is it a personal probability?
C. Suppose another friend has never tried the experiment but believes he has ESP and can guess correctly with probability .60. Is the value of .60 a relative-frequency probability or a personal probability. Explain
D. Suppose another friend guessed the color of 1000 cards and got 600 correct. The friend claims she has ESP and has a .60 probability of guessing correctly. Is the value of .60 a relative-frequency probability or a personal probability. Explain

It's been many years since I took a statistics class, so I don't remember all of the vocabulary.

However, when you have a 50-50 chance of getting the answer right, then the normal range will be somewhere between 30% and 70% correct answers.

The answer to part a) is 1/2

As for the others, I have never heard of "personal probability"

There are two kinds of probability:
1. Empirical Probability which is based on the results of experiments to collect data about an event
2. Mathematical Probability base on the concepts of mathematics

Any attempt to combine such ideas as ESP with the beautiful laws of Mathematics would be alien to most mathematicians.

A. In this case, you have a 50% chance of guessing the color correctly by chance. Since there are 26 red and 26 black cards, the odds of guessing the correct color on any given card is 26/52 = 1/2.

To calculate the probability of guessing the color correctly for multiple cards, you need to consider the independent nature of each guess. Since after each guess, the card is replaced and reshuffled, the probability remains the same for each guess. Therefore, the probability of guessing the color correctly for all cards is (1/2)^n, where n is the number of cards being guessed.

B. The answer in part A is based on the relative-frequency interpretation of probability. This interpretation assumes that the probability of an event can be inferred from the long-term relative frequency of its occurrence. In this case, the probability of guessing the color correctly is based on the relative frequency of red and black cards in the deck.

C. The value of 0.60 in this scenario is a personal probability. A personal probability is an individual's subjective belief or degree of confidence in the occurrence of an event. It is not based on long-term frequency or empirical data but rather on personal subjective assessment.

D. The value of 0.60 in this scenario is also a personal probability. Even though the friend claims to have ESP and a 0.60 probability of guessing correctly, this value is still a personal probability. It is based on their subjective belief or confidence in their guessing ability, rather than any empirical data or long-term frequency.