Final answer:
The probability of drawing a gold coin from a bucket with 350 coins, of which 5 are gold, is 1 in 70, or about 1.43%. Each drawing event is independent, meaning prior draws don't affect the probability of subsequent draws.
Step-by-step explanation:
The probability of pulling a gold coin from a bucket containing 350 coins where only 5 of them are gold can be calculated by dividing the number of gold coins by the total number of coins. Hence, the probability (P) is P(gold coin) = number of gold coins / total number of coins = 5 / 350 = 1/70. This simplifies to approximately 0.0143, meaning there is a 1.43% chance of selecting a gold coin on any given draw.
Understanding probability requires recognizing that each event is independent, and the likelihood of a particular outcome does not change regardless of past events. This is similar to the concept of a fair coin, where each toss is independent and has a 50% chance of landing as heads regardless of the previous tosses. Over time, the more we perform an experiment, the closer we'll get to the theoretical probability, as demonstrated in Pearson's coin toss experiment.