I am trying to solve a homework problem, and I am stuck in the following question: What is the probability of all trials to be successful in an infinite sequence of independent Bernoulli trials? The probability of success is given by p and of failure is (1-p). I would appreciate any help.
Probability of all trial success in infinite Bernoulli trials
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probability
1 Answers
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HINT: The probability of $n$ successes in a row is $p^n.$ What happens as $n\to\infty$? What if $p=1$? What if $p<1?$