Final answer:
To find the probability of having the number of heads flipped equal to four times the number of tails flipped when flipping a coin 35 times, we use the binomial probability formula and the fact that the coin is weighted so that it flips heads six times as often as tails.
Step-by-step explanation:
To find the probability of having the number of heads flipped equal to four times the number of tails flipped when flipping a coin 35 times, we need to first determine the probabilities of flipping a head and a tail. Since the coin is weighted so that it flips heads six times as often as it comes up tails, the probability of flipping a head is 6/7 and the probability of flipping a tail is 1/7.
Next, we need to calculate the probability of having the number of heads flipped equal to four times the number of tails flipped. This can be done using the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where X is the variable that represents the number of successes (in this case, the number of heads flipped), k is the desired number of successes (four times the number of tails flipped), n is the total number of trials (35), p is the probability of success (6/7), and (1-p) is the probability of failure (1/7).
Plugging in the values, we get:
P(X=4*tail flips) = C(35,4*tail flips) * (6/7)^(4*tail flips) * (1/7)^(35-(4*tail flips))
Therefore, the correct answer is (35/7) * (6/7)^(4*tail flips) * (1/7)^(35-(4*tail flips)), where tail flips can be any integer value between 0 and 8.