Final Answer:
a) The probability of getting all tails is 0.0078 (0.0078 rounded to 4 decimal places).
b) The probability of getting all heads is 0.0078 (0.0078 rounded to 4 decimal places).
Step-by-step explanation:
The probability of flipping a fair coin 7 times and getting all tails (or all heads) is the same and can be calculated using the formula for combinations.
To calculate the probability of getting all tails (or all heads), we must find the number of favorable outcomes over the total number of possible outcomes. The total number of possible outcomes when flipping a coin 7 times is 2^7, or 128.
The number of favorable outcomes is 1, as there is only one combination of all tails (or all heads). Therefore, when dividing the number of favorable outcomes (1) by the total number of possible outcomes (128), the probability of getting all tails (or all heads) when flipping a fair coin 7 times is 0.0078. When rounded to 4 decimal places, this probability is 0.0078.