Final answer:
To determine if a coin is fair, we need to compare the observed outcomes to the expected outcomes. We can calculate the probability of getting 37 or more heads when tossing a fair coin 100 times using binomial probability.
Step-by-step explanation:
In order to determine if a coin is fair, we need to compare the observed outcomes to the expected outcomes. For a fair coin, the probability of getting a head is 0.5. If a coin is tossed 100 times and 37 heads are observed, we can calculate the probability of getting 37 or more heads using binomial probability. If this probability is greater than 0.025 (97.5 percentile), we can infer that the coin is not fair.
The probability of getting 37 or more heads when tossing a fair coin 100 times can be calculated as follows:
P(X ≥ 37) = P(X = 37) + P(X = 38) + ... + P(X = 100)
Using binomial probability formula, P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where n is the number of trials (100), k is the number of successes (37), p is the probability of success (0.5), and C(n, k) is the binomial coefficient.
By calculating this probability, we can make an inference about whether the coin is fair or not.