Question

In a certain card game, the probability that a player is dealt a particular hand is 0.32 . Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 32 times? Why or why not? Choose the correct answer below.

A. The probability 0.32 means that exactly 32 out of every 100 dealt hands will be that particular hand. Yes, you will be dealt this hand exactly 32 times since the probability refers to short-term behavior, not long-term.
B. The probability 0.32 means that approximately 32 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 32 times since the probability refers to what is expected in the long-term, not short-term.
C. The probability 0.32 means that exactly 32 out of every 100 dealt hands will be that particular hand. Yes, you will be dealt this hand exactly 32 times since the probability refers to long-term behavior, not short-term.
D. The probability 0.32 means that approximately 32 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 32 times since the probability refers to what is expected in the short-term, not long-term.

Answer 1

The probability of 0.32 means that there is a theoretical chance of being dealt a specific hand in any single round. While you might expect to see approximately 32 occurrences of this hand in 100 plays, exact outcomes will vary and are not guaranteed due to randomness and the Law of Large Numbers.

Step-by-step explanation:

The probability of 0.32 in a certain card game means that there is a 32% chance that a player is dealt a particular hand during any single round of play. This probability is a theoretical probability describing what can be expected in the long-term, rather than precise outcomes in the short-term. If you play this card game 100 times, you are not guaranteed to be dealt this hand exactly 32 times. Instead, the number of times you're dealt the hand may vary due to randomness, but with a large number of trials, the actual frequency should approximate the theoretical probability.

The Law of Large Numbers indicates that as the number of trials increases, the relative frequency of getting that hand should get closer to 32%, but only in the long run. Short-term results could deviate substantially from the expected probability as each deal of cards is an independent event. The correct choice from the provided options would therefore be B: The probability 0.32 means that approximately 32 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 32 times since the probability refers to what is expected in the long-term, not short-term.