Final answer:
The probability of drawing a gold coin from a bucket of 350 coins, where 5 are gold, is 5/350. This concept demonstrates the same principles as in coin toss probabilities, where individual events may deviate from the expected outcome, but over many trials, the results will typically align with the expected probabilities.
Step-by-step explanation:
Understanding Probability in Coin Tosses
When we talk about the probability of pulling a gold coin from a bucket of coins, we refer to the chance or likelihood of a particular event happening - in this case, drawing one of the few gold coins rather than another type of coin. If there is a bucket with 350 coins, and 5 of them are gold, the probability of pulling out a gold coin is calculated by dividing the number of favorable outcomes (gold coins) by the total number of possible outcomes (total coins). Thus, the probability P of drawing a gold coin is P(gold) = 5/350.
The principle highlighted here is similar to what is observed in coin tosses. When a fair coin is tossed, each outcome (heads or tails) has an equal probability of 0.5, or 50 percent. Regardless of this theoretical probability, the real-world results can temporarily diverge from the expected outcomes. For example, flipping a coin twice may not necessarily lead to one head and one tail. However, as demonstrated by Pearson's experiment, where he tossed a coin 24,000 times, the relative frequency of heads obtained (just over 50 percent) was very close to the theoretical probability. This demonstrates the law of large numbers, asserting that as an experiment is conducted many times, the experimental probability tends to get closer to the theoretical probability.
While probability can guide us on what to expect over a long series of experiments, it does not predict short-term variations accurately. This is an important concept when calculating probabilities because it shows that while we can expect certain outcomes over many trials, individual trials can yield unexpected results. For instance, in our bucket of coins, even though the likelihood of drawing a gold coin is relatively low, it's still possible to draw one on the first try, much like it's also possible to flip a coin twice and get two heads in a row.