Final answer:
The probability of getting at most 1 tails after tossing a fair coin 8 times is 0.066, rounded to the nearest thousandth.
Step-by-step explanation:
When a fair coin is tossed 8 times, the probability of getting at most 1 tails can be calculated using the binomial probability formula.
In this case, we are looking for the probability of getting 0 tails (all heads) plus the probability of getting exactly 1 tails.
The probability of getting 0 tails (which is the same as getting 8 heads) for 8 tosses is calculated by (0.5)8.
The probability of getting exactly 1 tails (and therefore 7 heads) would be 8 × (0.5)7 × (0.5) since there are 8 different ways to arrange 1 tails amongst 8 flips.
Probability of 0 tails: (0.5)8 = 0.00390625
Probability of exactly 1 tails: 8 × (0.5)7 × (0.5) = 8 × 0.0078125 = 0.0625
Total probability (at most 1 tails) = Probability of 0 tails + Probability of exactly 1 tails = 0.00390625 + 0.0625 = 0.06640625
Round this to the nearest thousandth to get 0.066 as the final probability.