Question

a fair coin is flipped n times. give an expression for each of the probabilities below as a function of n. simplify your final expression as much as possible. (a) at least n - 1 flips come up heads.

Answer 1

To find the probability of at least n-1 flips coming up heads when a fair coin is flipped n times, consider two cases: all n flips come up heads, and exactly n-1 flips come up heads.

Step-by-step explanation:

To find the probability of at least n-1 flips coming up heads when a fair coin is flipped n times, we need to consider two cases:

1. All n flips come up heads
2. Exactly n-1 flips come up heads

Case 1: All n flips come up heads

In this case, the probability is simply 1, since the only outcome is that all flips come up heads.

Case 2: Exactly n-1 flips come up heads

In this case, we need to choose n-1 flips out of the n flips to be heads, and the remaining 1 flip to be tails. The probability of getting heads on a single flip is 1/2, so the probability of choosing n-1 flips out of n to be heads is (n choose n-1) * (1/2)^(n-1) * (1/2)^1 = n/2^n.

To find the overall probability, we add the probabilities of the two cases together: 1 + n/2^n.