Final answer:
The probability of flipping all heads or all tails in 10 coin flips is 1/512 or approximately 0.195%, as there is only one way to achieve each outcome out of the 1024 possible combinations of flips.
Step-by-step explanation:
The question asks about the probability of flipping either all heads or all tails when a coin is flipped 10 times. When a fair coin is tossed, there are two possible outcomes for each flip: heads (H) or tails (T). The probability of getting either heads or tails on a single flip is 1/2 (or 50%). The flips are independent events, meaning that the result of one flip does not affect the results of the other flips.
For all heads or all tails, there is only one way to achieve each of these outcomes (HHHHHHHHHH for all heads and TTTTTTTTTT for all tails). The total number of possible outcomes for flipping a coin 10 times is 210, or 1024. Therefore, the probability of getting all heads (1/1024) plus the probability of getting all tails (1/1024) equals 2/1024, which simplifies to 1/512.
So, the correct answer choice, representing the probability of getting either all heads or all tails, is therefore 1 divided by 512, or approximately 0.195%.