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

its adding 5.5 each time

step-by-step explanation:

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %