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).