Final answer:
P{N ≥ i} is the probability of flipping a coin and getting the first head on the i-th flip or later. For a fair coin with a probability of 0.5 for each side, the probability can be calculated as (0.5)^(i-1). This is based on multiplying the probability of getting tails on all previous flips before the i-th flip.
Step-by-step explanation:
The question posted by the student concerns the probability of the number of coin flips needed to obtain a head. Specifically, the student asks for P{N ≥ i}, meaning the probability that flipping the coin results in getting the first head on the i-th flip or later. To find this probability, we consider the case of flipping a coin that has only two outcomes: heads (H) or tails (T), with equal probability of 0.5 each (assuming a fair coin).
To calculate P{N ≥ i}, we have to consider that we are tossing tails for (i-1) times before we get the first head. Because the flips are independent events, we can multiply the probabilities of individual flips. Hence, the probability of getting a tail on any given flip is 0.5, and the probability of getting tails (i-1) times in a row is (0.5)^(i-1). Since we are seeking the probability of at least i flips, we need to consider every scenario from i flips to infinity, which theoretically continues the chain of 0.5 probabilities infinitely.
Thus, the probability of getting the first head on the i-th flip or later is just the continuation of getting tails, which can be stated as:
P{N ≥ i} = (0.5)^(i-1)