Question

A single card is chosen at random from a deck of 52 cards, the probability that a club card is selected is 1/4. Does this probability mean that, if you choose a card at random 8 times, a club will appear twice? If not, what does it mean?

Probability?

Answer 1

Answer: "No"

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the law only applies (as the name indicates) when a large number of observations is considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced" by the others

Example:

For example, a fair coin toss is a Bernoulli trial. When a fair coin is flipped once, the theoretical probability that the outcome will be heads is equal to 1/2. Therefore, according to the law of large numbers, the proportion of heads in a "large" number of coin flips "should be" roughly 1/2. In particular, the proportion of heads after n flips will almost surely converge to 1/2 as n approaches infinity.

Solution of given problem:

Similarly if we select a single card random from a deck of 52 cards for large number of times proportion of a club card should be roughly 1/4,that is the proportion of getting a club card after n flips will almost surely converge to 1/4 as n approaches infinity.