Acoin 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 h}. compute p(c1). next, suppose that c2 = {c : c is h or h}. compute p(c2), p(c1 ∩ c2), and p(c1 ∪ c2).

Step-by-step explanation:

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.

Now, observe that

Then

and

3/6 chance

step-by-step explanation:

half of the nubers are odd numbers (1,3,5) which in that case if you would be told to simplify it would be 1/2