A coin flip determines who gets the ball first at the beginning of a football game, with the visiting team calling heads or tails. The captain of one particular team always calls heads. In the first four games as visitor of a season, find the probability that his team
(a) Wins the toss three times.
(b) Loses the toss four times.
(c) Wins the toss more than three times.
(d) Loses the toss no more than three times.
(e) Loses the toss at least three times.
Write your answers in exact, simplified form.
Part 1 of 5
(a) The probability that the team wins the toss three times is
Part 2 of 5
(b) The probability that the team loses the toss all four times is

Step 1 ：The coin flip is a binomial experiment where there are only two outcomes - heads or tails. The probability of getting heads (winning the toss) or tails (losing the toss) is 0.5 each.

Step 2 ：For part (a), we need to find the probability of winning the toss exactly 3 times in 4 trials. This is a binomial probability problem which can be solved using the formula: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the combination of n items taken k at a time, p is the probability of success on a single trial, n is the number of trials, k is the number of successes.

Step 3 ：Substituting the given values into the formula, we get \(P(X=3) = C(4, 3) * (0.5^3) * ((1-0.5)^(4-3))\). Simplifying this, we get a probability of 0.25.

Step 4 ：For part (b), we need to find the probability of losing the toss all four times. This is simply the probability of getting tails 4 times in a row, which can be calculated as \((0.5)^4\).

Step 5 ：Simplifying this, we get a probability of 0.0625.

Step 6 ：Final Answer: (a) The probability that the team wins the toss three times is \(\boxed{0.25}\). (b) The probability that the team loses the toss all four times is \(\boxed{0.0625}\).