Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The probability of an event occuring N times in a day is $ P[N=n] = \frac{1}{2^(n)} where 0\le n $. The number of times an event ocurrs in one day is independent of the number of times the event has happened on any past day.

What is the probability that the event will occur exactly 5 times during any two-day period?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

There are six combinations of events that add to 5 over the two day period. These six events occur with the probability below.

$ 2[(1)(\frac{1}{2^5}) + (\frac{1}{2})(\frac{1}{2^4}) + (\frac{1}{2^2})(\frac{1}{2^3})]$

$= \frac{3}{2^4}$

$=\frac{3}{16}$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.