a) Let A and B be mutually exclusive events. Independent trials of the experiment are performed to see which one of the two occurs first. What is the probability that event A occurs before event. B?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Consider a repeated experiment with sample space S, and two events A and B with probabilities p_a and p_b, respectively. (All answers should be in terms of p_a and p_b.)

 

a) Let A and B be mutually exclusive events. Independent trials of the experiment are
performed to see which one of the two occurs first. What is the probability that event
A occurs before event B?
b) Next solve a similar problem for the case where A and B are independent events (and
not mutually exclusive). What is the probability that event A occurs before event B?
(Note that now we must allow for the possibility that they occur simultaneously, as
they are not mutually exclusive).
Transcribed Image Text:a) Let A and B be mutually exclusive events. Independent trials of the experiment are performed to see which one of the two occurs first. What is the probability that event A occurs before event B? b) Next solve a similar problem for the case where A and B are independent events (and not mutually exclusive). What is the probability that event A occurs before event B? (Note that now we must allow for the possibility that they occur simultaneously, as they are not mutually exclusive).
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