Final answer:
To find the probability of getting exactly 6 heads when a fair coin is tossed 7 times, we can use the formula for the probability of a specific number of successes in a binomial experiment. The probability of getting exactly 6 heads is approximately 0.109 or 10.9%.
Step-by-step explanation:
To find the probability of getting exactly 6 heads when a fair coin is tossed 7 times, we can use the formula for the probability of a specific number of successes in a binomial experiment. In this case, the probability of getting a head on any single toss is 0.5, since the coin is fair. The probability of getting exactly 6 heads is calculated as:
P(6 heads) = C(7, 6) * (0.5)^6 * (0.5)^(7-6), where C(7, 6) is the number of ways to choose 6 heads out of 7 tosses.
Using the combination formula C(n, r) = n! / (r! * (n-r)!), we can calculate C(7, 6) = 7! / (6! * (7-6)!). Evaluating this expression gives C(7, 6) = 7. Plugging this into our probability formula, we get:
P(6 heads) = 7 * (0.5)^6 * (0.5)^(7-6) = 7 * (0.5)^7 = 0.109375.
Therefore, the probability of getting exactly 6 heads when a fair coin is tossed 7 times is approximately 0.109 or 10.9%.