Final answer:
The probability of flipping a coin 10 times and getting tails 8 times is 4.4%.
Step-by-step explanation:
When flipping a coin, the probability of getting tails is 50%. To calculate the probability of getting tails 8 times out of 10 flips, we can use the binomial probability formula which is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
where P(x) is the probability of getting x successes, n is the number of trials, p is the probability of success in a single trial, and C(n, x) is the number of combinations of n things taken x at a time. In this case, n=10, x=8, and p=0.5. Plugging in these values, we get:
P(8) = C(10, 8) * 0.5^8 * (1-0.5)^(10-8) = 45 * 0.5^8 * 0.5^2 = 45 * 0.5^10 = 0.0439453125
To convert this decimal to a percentage, we multiply by 100:
P(8) = 0.0439453125 * 100 = 4.39453125%
Therefore, the probability of flipping a coin 10 times and getting tails 8 times, rounded to the nearest tenth of a percent, is approximately 4.4%.