Final answer:
The value of n, the probability of getting exactly one head in ten coin flips, is approximately 105.
Step-by-step explanation:
To find the value of n, we need to determine the probability of getting exactly one head in ten coin flips. In this case, n represents the number of successful outcomes, which is getting exactly one head, and 210 represents the total number of possible outcomes, which is flipping the coin ten times.
The probability of getting exactly one head in ten flips can be calculated using the binomial probability formula:
p(x) = C(n,x) * p^x * q^(n-x)
Where:
- p(x) is the probability of getting exactly x successes
- C(n,x) is the number of ways to choose x successes out of n trials
- p is the probability of success on a single trial
- q is the probability of failure on a single trial
In this case, we have n = 10 and p = 1/2 because the coin is fair. Therefore, q = 1 - p = 1/2 as well. Substituting these values into the formula, we get:
p(1) = C(10,1) * (1/2)^1 * (1/2)^(10-1)
Simplifying further:
p(1) = 10 * (1/2) * (1/2)^9 = 10/2^10 = 10/1024 = 5/512
So, the probability of getting exactly one head is 5/512. Comparing this to the given probability of n/210, we can conclude that n = 5/512 * 210 = 1050/512 = 105/51. Therefore, the value of n is approximately 105.