Suppose a coin is flipped 2 times, the sample space consists of 4 sample points. S = {TT, TH, HT, HH} Suppose a coin is flipped 3 times, the sample space consists of 8 sample points. S = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH} Suppose a coin is flipped 25 times, the sample space consists of? How to calculate this, what’s the formula? Must be very simple, but not being able to crack quickly. Many thanks in advance.
The sample space would be 2^25. It is an exponential growth in your sample space. The way to think of it is: The base is the number potential outcomes (head or tail) and the exponent is the number of times (25 flips)
An interesting way of looking at it: If a coin is flipped N times, imagine the number of ways you can fill N slots with the letter ‘H’ or "T’ with repetition. From combination theory, its 2^N