Final answer:
To estimate the probability of getting between 40 and 50 heads when tossing a biased coin 400 times, you can use the binomial distribution formula. This formula calculates the probability of getting exactly k heads in n trials.
Step-by-step explanation:
To estimate the probability of getting between 40 and 50 heads when tossing a biased coin 400 times, we need to use the binomial distribution formula. The formula is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where:
- P(X = k) is the probability of getting exactly k heads
- C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient)
- p is the probability of getting a head, which is 1/10 in this case
- n is the number of trials, which is 400
- k is the number of heads we want to get, which ranges from 40 to 50
To estimate the probability of getting between 40 and 50 heads, we need to calculate P(X = 40) + P(X = 41) + ... + P(X = 50) using the binomial distribution formula.