Final answer:
To find the probability of getting nine or more heads when a fair coin is flipped 11 times, we add the probabilities of getting exactly 9, 10, and 11 heads. The formula used for calculating the probability is P(k heads) = (n choose k) * (p^k) * (q^(n-k)), where n is the number of flips, k is the number of heads, p is the probability of heads (0.5), and q is the probability of tails (0.5). By applying this formula, we can calculate the probabilities and add them to find the answer.
Step-by-step explanation:
To find the probability of getting nine or more heads when a fair coin is flipped 11 times, we need to calculate the probability of getting exactly 9 heads, exactly 10 heads, and exactly 11 heads, and then add them up.
The probability of getting exactly k heads in n flips of a fair coin is given by the formula:
P(k heads) = (n choose k) * (p^k) * (q^(n-k))
Where n is the number of flips, k is the number of heads, p is the probability of heads (0.5), and q is the probability of tails (0.5).
Using this formula, we can calculate:
P(9 heads) = (11 choose 9) * (0.5^9) * (0.5^2) = 55 * 0.5^11
P(10 heads) = (11 choose 10) * (0.5^10) * (0.5^1) = 11 * 0.5^11
P(11 heads) = (11 choose 11) * (0.5^11) * (0.5^0) = 1 * 0.5^11
Finally, we add these three probabilities together to get the probability of getting nine or more heads:
P(nine or more heads) = P(9 heads) + P(10 heads) + P(11 heads)