When flipping an unbalanced coin with different probabilities for heads and tails, one can use the binomial probability formula to calculate the probabilities of specific outcomes over multiple flips.
The question involves calculating the probability of different outcomes when flipping an unbalanced coin several times. Since the coin has a 55% chance of landing heads and a 45% chance of landing tails, we can use the binomial probability formula to find the required probabilities.
a. The probability of getting seven heads when flipping the coin seven times is (0.55)^7 since each flip is independent and has the same probability of heads.
b. The probability of getting at least one head can be calculated by subtracting the probability of getting no heads from 1, which is 1 - (0.45)^7.
c. The probability of getting exactly three heads is given by the binomial probability formula: (7 choose 3) * (0.55)^3 * (0.45)^4.
d. To calculate the probability of getting more heads than tails, sum the probabilities of getting 4, 5, 6, and 7 heads, which would each result in more heads than tails.
So, using the given probabilities, we can calculate each scenario with the appropriate formulas to find the final answers.