A coin is to be tossed as many times as necessary to turn up one head. Thus the elements c of the sample space C are H, TH, TTH,
TTTH, and so forth. Let the probability set function P assign to these elements the respective probabilities 1 2 , 1 4 , 1 8 , 1 16 , and so forth. Show that P(C) = 1. Let C1 = {c : c is H,TH,TTH,TTTH, or TTTTH}. Compute P(C1). Next, suppose that C2 = {c : c is TTTTH or TTTTTH}. Compute P(C2), P(C1 ∩ C2), and P(C1 ∪ C2).
As stated in the question, the probability to toss a coin and turn up heads in the first try is , in the second is , in the third is and so on. Then, P(C) is given by the next sum:
This is a geometric series with factor . Then is convergent to . With this we have proved that P(C)=1.
Katja would be the straight line and joels line would show sections that stop going up it would intersect at some point because katja is constantly moving while joel takes breaks in-between