Question

Consider the event of a coin being flipped times. If that event is repeated ten thousand different times, it is expected that the event would result in about enter your response here time(s).

Answer 1

On average, the event of a coin being flipped 10,000 times is expected to result in about 5,000 heads.

Step-by-step explanation:

In a fair coin flip, there are two possible outcomes: heads (H) or tails (T), each with a probability of 0.5. The expected value (mean) of a single coin flip can be calculated as the sum of the products of each outcome and its probability. For a fair coin, this is given by:

`\[E(X) = (0.5 * 1) + (0.5 * 0) = 0.5.\]`

Now, if the coin is flipped 10,000 times, the expected total number of heads (H) can be found by multiplying the expected value of a single flip by the number of flips:

`\[E(X_{\text{total}}) = E(X) * n = 0.5 * 10,000 = 5,000.\]`

This means, on average, we can expect 5,000 heads in 10,000 coin flips. It's important to note that this is a theoretical average, and in any specific set of 10,000 flips, the actual number of heads may deviate from this expected value due to the inherent randomness of each individual flip. However, as the number of flips increases, the observed proportion of heads is likely to converge towards the expected probability of 0.5. This is a fundamental concept in probability theory known as the Law of Large Numbers.