Final answer:
The probability of getting exactly 6 heads when a biased coin is tossed 10 times is approximately 0.2126, or 21.26%.
Step-by-step explanation:
To find the probability of getting exactly 6 heads when a biased coin is tossed 10 times, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n-k)
Where:
- n is the number of trials (10 in this case)
- k is the number of successful outcomes (6 heads in this case)
- p is the probability of success (0.55 in this case)
- C(n, k) is the number of ways to choose k successes from n trials (10 choose 6, which is 210 in this case)
Using the values in the formula, we can calculate:
P(X = 6) = C(10, 6) * (0.55)^6 * (1 - 0.55)^(10-6)
P(X = 6) = 210 * (0.55)^6 * (0.45)^4
P(X = 6) ≈ 0.2126
Therefore, the probability of getting exactly 6 heads when the coin is tossed 10 times is approximately 0.2126, or 21.26%.