Question

When you flip 4 coins, the probability of getting half heads is 0.38. Likewise, the probability is 0.25 of finding that one fourth of the coins is heads. So, with four coins, the most likely outcome (the most probably state) is getting half heads, BUT thechance of getting one head (or one tail and three heads as well) is not all that much smaller, at 0.25. The charts show the probabilities for getting various fractions of heads for flipping four and for flipping eight coins. Describe the differences between the cases of four coins and eight coins with respect to how the probability of getting one-fourth heads compares to one-half heads changes when going from four to eight coins.

Answer 1

The probability distribution of flipping coins changes as the number of coins increases due to the law of large numbers. The probability of getting half heads is the highest when flipping four coins, whereas the probability distribution broadens with eight coins, making specific outcomes less likely.

Step-by-step explanation:

When analyzing the probability of outcomes when flipping coins, we can compare the cases of flipping four coins to flipping eight coins. When flipping four coins, the most likely outcome is two heads, with a probability of 0.38. The probability of getting one head, which is one-fourth of the coins, has a probability of 0.25. However, these probabilities might change when flipping eight coins because as the number of coin flips increases, the distribution of outcomes tends to become more even due to the law of large numbers.

Tossing a fair coin should theoretically result in 50 percent heads over the long term, as demonstrated by Karl Pearson's experiment which approximated the theoretical probability after 24,000 coin tosses. When moving to eight coins, the probability distribution for getting different fractions of heads will widen, meaning that it's less likely to get a specific outcome (in terms of fractions of heads) because there are more possible combinations (microstates).

Overall, while the exact probabilities for eight coins are not provided, we can expect that the probability of getting exactly half heads will decrease since there are more total combinations possible, and the probability for one-fourth heads will also change but without specific numbers, we cannot determine the precise probabilities.

Answer 2

Step-by-step explanation:

The probability would be twice as large for eight coins I think