In a probability experiment, the theoretical probability of pulling two candies of the same color from a jar was calculated to be 0.25. If you pulled out a pair of candies 5 times, would you expect that your probability of pulling a pair of the same color would also be 0.25? What about if you pulled out 500 pairs of candies? Answer in at least 2-3 complete sentences, and justify your answer using the Law of Large Numbers. The Law of Large Numbers: As the number of repetitions of an experiment is increased, the relative frequency obtained in the experiment tends to become closer and closer to the theoretical probability. Even though the outcomes do not happen according to any set pattern or order, overall, the long-term observed relative frequency will approach the theoretical probability.

- No, the probability of pulling out a pair of candle of similar colours 5 times in a row isn't the same as pulling it out once; for 5 times in a row, it is (the probability of doing it once)⁵, that is, 0.25⁵ = 0.0009765625

- If you now pull out candles 500 times, the probability becomes 0.25⁵⁰⁰ = (9.333 × 10⁻³⁰²); the theoretical probability becomes smaller as the number of trials becomes bigger.

- And with the backing of the law of large numbers, as the number of trials become bigger and the theoretical probability becomes smaller, the number of times a pair of candles with similar colours would be picked becomes smaller when compared to the total number of large trials.

Step-by-step explanation:

If the probability of pulling a pair of candles of the same colours is 0.25,

The probability of pulling a pair of candles twice in a row would be 0.25 × 0.25 = 0.0625

The probability of pulling a pair of candles thrice in a row would be 0.25 × 0.25 × 0.25 = 0.015625

For n times in a row = 0.25ⁿ

The theoretical probability becomes smaller as the number of trials becomes bigger.

And with the backing of the law of large numbers, as the number of trials become bigger and the probability becomes smaller, the number of times a pair of candles with similar colours would be picked becomes smaller when compared to the total number of large trials.